WorldWideScience

Sample records for quantum operators

  1. Cohering power of quantum operations

    Energy Technology Data Exchange (ETDEWEB)

    Bu, Kaifeng, E-mail: bkf@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China); Kumar, Asutosh, E-mail: asukumar@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019 (India); Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094 (India); Zhang, Lin, E-mail: linyz@zju.edu.cn [Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 (China); Wu, Junde, E-mail: wjd@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China)

    2017-05-18

    Highlights: • Quantum coherence. • Cohering power: production of quantum coherence by quantum operations. • Study of cohering power and generalized cohering power, and their comparison for differentmeasures of quantum coherence. • Operational interpretation of cohering power. • Bound on cohering power of a generic quantum operation. - Abstract: Quantum coherence and entanglement, which play a crucial role in quantum information processing tasks, are usually fragile under decoherence. Therefore, the production of quantum coherence by quantum operations is important to preserve quantum correlations including entanglement. In this paper, we study cohering power–the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.

  2. Schmidt number for quantum operations

    International Nuclear Information System (INIS)

    Huang Siendong

    2006-01-01

    To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided

  3. Heat transfer operators associated with quantum operations

    International Nuclear Information System (INIS)

    Aksak, C; Turgut, S

    2011-01-01

    Any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system. If the extension used is a heat bath in thermal equilibrium, the concomitant change in the state of the bath necessarily implies a heat exchange with it. The dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a Hermitian operator, which is named as the heat transfer operator (HTO). The purpose of this paper is to investigate the relation between the HTOs and the associated quantum operations. Since any given quantum operation on a system can be realized by different baths and unitaries, many different HTOs are possible for each quantum operation. On the other hand, there are also strong restrictions on the HTOs which arise from the unitarity of the transformations. The most important of these is the Landauer erasure principle. This paper is concerned with the question of finding a complete set of restrictions on the HTOs that are associated with a given quantum operation. An answer to this question has been found only for a subset of quantum operations. For erasure operations, these characterizations are equivalent to the generalized Landauer erasure principle. For the case of generic quantum operations, however, it appears that the HTOs obey further restrictions which cannot be obtained from the entropic restrictions of the generalized Landauer erasure principle.

  4. Fixed points of quantum operations

    International Nuclear Information System (INIS)

    Arias, A.; Gheondea, A.; Gudder, S.

    2002-01-01

    Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation, and quantum information theory. If an operator A is invariant under a quantum operation φ, we call A a φ-fixed point. Physically, the φ-fixed points are the operators that are not disturbed by the action of φ. Our main purpose is to answer the following question. If A is a φ-fixed point, is A compatible with the operation elements of φ? We shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes. Our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von Neumann algebras

  5. General description of discriminating quantum operations

    International Nuclear Information System (INIS)

    Zhang Ke-Jia; Gao Fei; Qin Su-Juan; Wen Qiao-Yan; Zhu Ping; Guo Fen-Zhuo

    2011-01-01

    The discrimination of quantum operations plays a key role in quantum information and computation. Unlike discriminating quantum states, it has some special properties which can be carried out in practice. In this paper, we provide a general description of discriminating quantum operations. Concretely speaking, we describe the distinguishability between quantum operations using a measure called operator fidelity. It is shown that, employing the theory of operator fidelity, we can not only verify some previous results to discriminate unitary operations, but also exhibit a more general discrimination condition. We further apply our results to analysing the security of some quantum cryptographic protocols and discuss the realization of our method using well-developed quantum algorithms. (general)

  6. Density operators in quantum mechanics

    International Nuclear Information System (INIS)

    Burzynski, A.

    1979-01-01

    A brief discussion and resume of density operator formalism in the way it occurs in modern physics (in quantum optics, quantum statistical physics, quantum theory of radiation) is presented. Particularly we emphasize the projection operator method, application of spectral theorems and superoperators formalism in operator Hilbert spaces (Hilbert-Schmidt type). The paper includes an appendix on direct sums and direct products of spaces and operators, and problems of reducibility for operator class by using the projection operators. (author)

  7. Quantum Strategies and Local Operations

    Science.gov (United States)

    Gutoski, Gus

    2010-02-01

    This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game. In Part II we establish several properties of a class of quantum operations that can be implemented locally with shared quantum entanglement or classical randomness. In particular, we establish the existence of a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. The existence of this ball is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. We also provide characterizations of local operations in terms of linear functionals that are positive and "completely" positive on a certain cone of Hermitian operators, under a natural notion of complete positivity appropriate to that cone. We end the thesis with a discussion of the properties of no-signaling quantum operations.

  8. Entropic cohering power in quantum operations

    Science.gov (United States)

    Xi, Zhengjun; Hu, Ming-Liang; Li, Yongming; Fan, Heng

    2018-02-01

    Coherence is a basic feature of quantum systems and a common necessary condition for quantum correlations. It is also an important physical resource in quantum information processing. In this paper, using relative entropy, we consider a more general definition of the cohering power of quantum operations. First, we calculate the cohering power of unitary quantum operations and show that the amount of distributed coherence caused by non-unitary quantum operations cannot exceed the quantum-incoherent relative entropy between system of interest and its environment. We then find that the difference between the distributed coherence and the cohering power is larger than the quantum-incoherent relative entropy. As an application, we consider the distributed coherence caused by purification.

  9. Controllable conditional quantum oscillations and quantum gate operations in superconducting flux qubits

    International Nuclear Information System (INIS)

    Chen Aimin; Cho Samyoung

    2011-01-01

    Conditional quantum oscillations are investigated for quantum gate operations in superconducting flux qubits. We present an effective Hamiltonian which describes a conditional quantum oscillation in two-qubit systems. Rabi-type quantum oscillations are discussed in implementing conditional quantum oscillations to quantum gate operations. Two conditional quantum oscillations depending on the states of control qubit can be synchronized to perform controlled-gate operations by varying system parameters. It is shown that the conditional quantum oscillations with their frequency synchronization make it possible to operate the controlled-NOT and -U gates with a very accurate gate performance rate in interacting qubit systems. Further, this scheme can be applicable to realize a controlled multi-qubit operation in various solid-state qubit systems. (author)

  10. Consistent histories and operational quantum theory

    International Nuclear Information System (INIS)

    Rudolph, O.

    1996-01-01

    In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general comments about it. We investigate to what extent the consistent histories scheme is compatible with the results of the operational formulation of quantum mechanics. According to the operational approach, nonrelativistic quantum mechanics is most generally formulated in terms of effects, states, and operations. We formulate a generalized consistent histories theory using the concepts and the terminology which have proven useful in the operational formulation of quantum mechanics. The logical rule of the logical interpretation of quantum mechanics is generalized to the present context. The algebraic structure of the generalized theory is studied in detail

  11. Simulation of n-qubit quantum systems. III. Quantum operations

    Science.gov (United States)

    Radtke, T.; Fritzsche, S.

    2007-05-01

    During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 processor with ⩾2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems

  12. Operational interpretations of quantum discord

    International Nuclear Information System (INIS)

    Cavalcanti, D.; Modi, K.; Aolita, L.; Boixo, S.; Piani, M.; Winter, A.

    2011-01-01

    Quantum discord quantifies nonclassical correlations beyond the standard classification of quantum states into entangled and unentangled. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum-state-merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.

  13. Adding control to arbitrary unknown quantum operations

    Science.gov (United States)

    Zhou, Xiao-Qi; Ralph, Timothy C.; Kalasuwan, Pruet; Zhang, Mian; Peruzzo, Alberto; Lanyon, Benjamin P.; O'Brien, Jeremy L.

    2011-01-01

    Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity. PMID:21811242

  14. Nuclear spin states and quantum logical operations

    International Nuclear Information System (INIS)

    Orlova, T.A.; Rasulov, E.N.

    2006-01-01

    Full text: To build a really functional quantum computer, researchers need to develop logical controllers known as 'gates' to control the state of q-bits. In this work , equal quantum logical operations are examined with the emphasis on 1-, 2-, and 3-q-bit gates.1-q-bit quantum logical operations result in Boolean 'NOT'; the 'NOT' and '√NOT' operations are described from the classical and quantum perspective. For the 'NOT' operation to be performed, there must be a means to switch the state of q-bits from to and vice versa. For this purpose either a light or radio pulse of a certain frequency can be used. If the nucleus has the spin-down state, the spin will absorb a portion of energy from electromagnetic current and switch into the spin-up state, and the radio pulse will force it to switch into state. An operation thus described from purely classical perspective is clearly understood. However, operations not analogous to the classical type may also be performed. If the above mentioned radio pulses are only half the frequency required to cause a state switch in the nuclear spin, the nuclear spin will enter the quantum superposition state of the ground state (↓) and excited states (↑). A recurring radio pulse will then result in an operation equivalent to 'NOT', for which reason the described operation is called '√NOT'. Such an operation allows for the state of quantum superposition in quantum computing, which enables parallel processing of several numbers. The work also treats the principles of 2-q-bit logical operations of the controlled 'NOT' type (CNOT), 2-q-bit (SWAP), and the 3-q-bit 'TAFFOLI' gate. (author)

  15. Operator quantum error-correcting subsystems for self-correcting quantum memories

    International Nuclear Information System (INIS)

    Bacon, Dave

    2006-01-01

    The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures

  16. Quantum Logical Operations on Encoded Qubits

    International Nuclear Information System (INIS)

    Zurek, W.H.; Laflamme, R.

    1996-01-01

    We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to correct for 1-bit errors which either preexisted or occurred in the course of operation. The logical operations we consider allow one to carry out the vast majority of the steps in the quantum factoring algorithm. copyright 1996 The American Physical Society

  17. Generation of quantum logic operations from physical Hamiltonians

    International Nuclear Information System (INIS)

    Zhang Jun; Whaley, K. Birgitta

    2005-01-01

    We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all R z -equivalence classes of single-qubit operations, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local-equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes

  18. Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

    African Journals Online (AJOL)

    Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

  19. Quantum operations, state transformations and probabilities

    International Nuclear Information System (INIS)

    Chefles, Anthony

    2002-01-01

    In quantum operations, probabilities characterize both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure→pure state transformations, covering both probabilistic and deterministic cases. We then discuss the role of majorization in describing the dynamics of mixing in quantum operations. The conditions for mixing enhancement for all initial states are derived. We show that mixing is monotonically decreasing for deterministic pure→pure transformations, and discuss the relationship between these transformations and deterministic local operations with classical communication entanglement transformations

  20. Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

    International Nuclear Information System (INIS)

    Yang, C.-D.

    2006-01-01

    This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schroedinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → p = -ih∇, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov-Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion

  1. Radon-Nikodym derivatives of quantum operations

    International Nuclear Information System (INIS)

    Raginsky, Maxim

    2003-01-01

    Given a completely positive (CP) map T, there is a theorem of the Radon-Nikodym type [W. B. Arveson, Acta Math. 123, 141 (1969); V. P. Belavkin and P. Staszewski, Rep. Math. Phys. 24, 49 (1986)] that completely characterizes all CP maps S such that T-S is also a CP map. This theorem is reviewed, and several alternative formulations are given along the way. We then use the Radon-Nikodym formalism to study the structure of order intervals of quantum operations, as well as a certain one-to-one correspondence between CP maps and positive operators, already fruitfully exploited in many quantum information-theoretic treatments. We also comment on how the Radon-Nikodym theorem can be used to derive norm estimates for differences of CP maps in general, and of quantum operations in particular

  2. Calculating the C operator in PT-symmetric quantum mechanics

    International Nuclear Information System (INIS)

    Bender, C.M.

    2004-01-01

    It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT-symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory. (author)

  3. A Perron-Frobenius Type of Theorem for Quantum Operations

    Science.gov (United States)

    Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

    2017-10-01

    We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

  4. Operational quantum theory without predefined time

    International Nuclear Information System (INIS)

    Oreshkov, Ognyan; Cerf, Nicolas J

    2016-01-01

    The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures. (paper)

  5. Private quantum subsystems and quasiorthogonal operator algebras

    International Nuclear Information System (INIS)

    Levick, Jeremy; Kribs, David W; Pereira, Rajesh; Jochym-O’Connor, Tomas; Laflamme, Raymond

    2016-01-01

    We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the n-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory. (paper)

  6. Compton Operator in Quantum Electrodynamics

    International Nuclear Information System (INIS)

    Garcia, Hector Luna; Garcia, Luz Maria

    2015-01-01

    In the frame in the quantum electrodynamics exist four basic operators; the electron self-energy, vacuum polarization, vertex correction, and the Compton operator. The first three operators are very important by its relation with renormalized and Ward identity. However, the Compton operator has equal importance, but without divergence, and little attention has been given it. We have calculated the Compton operator and obtained the closed expression for it in the frame of dimensionally continuous integration and hypergeometric functions

  7. Algebraic quantization, good operators and fractional quantum numbers

    International Nuclear Information System (INIS)

    Aldaya, V.; Calixto, M.; Guerrero, J.

    1996-01-01

    The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the failure of the Ehrenfest theorem is clarified in terms of the already defined notion of good (and bad) operators. The analysis of constrained Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for quantum operators without classical analogue and for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring anomalous operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively. (orig.)

  8. Universal programmable quantum circuit schemes to emulate an operator

    Energy Technology Data Exchange (ETDEWEB)

    Daskin, Anmer; Grama, Ananth; Kollias, Giorgos [Department of Computer Science, Purdue University, West Lafayette, Indiana 47907 (United States); Kais, Sabre [Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); Qatar Environment and Energy Research Institute, Doha (Qatar)

    2012-12-21

    Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e{sup -iHt} for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.

  9. Universal programmable quantum circuit schemes to emulate an operator

    International Nuclear Information System (INIS)

    Daskin, Anmer; Grama, Ananth; Kollias, Giorgos; Kais, Sabre

    2012-01-01

    Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix–which can be non-unitary–in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e −iHt for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.

  10. New Hamiltonian constraint operator for loop quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

    2015-12-17

    A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  11. New Hamiltonian constraint operator for loop quantum gravity

    Directory of Open Access Journals (Sweden)

    Jinsong Yang

    2015-12-01

    Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  12. Quantum operations: technical or fundamental challenge?

    International Nuclear Information System (INIS)

    Mielnik, Bogdan

    2013-01-01

    A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as ‘operation factories’ transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract δ-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov–Bohm criticism of the time–energy uncertainty principle, while some others may verify the existence of fundamental precision limits of the position measurements or the reality of ‘non-commutative geometries’. (paper)

  13. Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces

    International Nuclear Information System (INIS)

    Chu, Chong-Sun; Zumino, B.

    1995-01-01

    The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail

  14. Random unitary operations and quantum Darwinism

    International Nuclear Information System (INIS)

    Balaneskovic, Nenad

    2016-01-01

    We study the behavior of Quantum Darwinism (Zurek, Nature Physics 5, 181-188 (2009)) within the iterative, random unitary operations qubit-model of pure decoherence (Novotn'y et al, New Jour. Phys. 13, 053052 (2011)). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system from the point of view of its environment, is not a generic phenomenon, but depends on the specific form of initial states and on the type of system-environment interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial initial states of environment that allow to store information about an open system of interest and its pointer-basis with maximal efficiency. Furthermore, we investigate the behavior of Quantum Darwinism after introducing dissipation into the iterative random unitary qubit model with pure decoherence in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)) and reconstruct the corresponding dissipative attractor space. We conclude that in Zurek's qubit model Quantum Darwinism depends on the order in which pure decoherence and dissipation act upon an initial state of the entire system. We show explicitly that introducing dissipation into the random unitary evolution model in general suppresses Quantum Darwinism (regardless of the order in which decoherence and dissipation are applied) for all positive non-zero values of the dissipation strength parameter, even for those initial state configurations which, in Zurek's qubit model and in the random unitary model with pure decoherence, would lead to Quantum Darwinism. Finally, we discuss what happens with Quantum Darwinism after introducing into the iterative random unitary qubit model with pure decoherence (asymmetric) dissipation and dephasing, again in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)), and reconstruct the corresponding

  15. Operator methods in quantum mechanics

    CERN Document Server

    Schechter, Martin

    2003-01-01

    This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q

  16. Neural implementation of operations used in quantum cognition.

    Science.gov (United States)

    Busemeyer, Jerome R; Fakhari, Pegah; Kvam, Peter

    2017-11-01

    Quantum probability theory has been successfully applied outside of physics to account for numerous findings from psychology regarding human judgement and decision making behavior. However, the researchers who have made these applications do not rely on the hypothesis that the brain is some type of quantum computer. This raises the question of how could the brain implement quantum algorithms other than quantum physical operations. This article outlines one way that a neural based system could perform the computations required by applications of quantum probability to human behavior. Copyright © 2017 Elsevier Ltd. All rights reserved.

  17. On the quantum Landau collision operator and electron collisions in dense plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Daligault, Jérôme, E-mail: daligaul@lanl.gov [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

    2016-03-15

    The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

  18. On the quantum Landau collision operator and electron collisions in dense plasmas

    Science.gov (United States)

    Daligault, Jérôme

    2016-03-01

    The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

  19. Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

    International Nuclear Information System (INIS)

    Yoshida, Beni

    2011-01-01

    Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.

  20. Operational resource theory of total quantum coherence

    Science.gov (United States)

    Yang, Si-ren; Yu, Chang-shui

    2018-01-01

    Quantum coherence is an essential feature of quantum mechanics and is an important physical resource in quantum information. Recently, the resource theory of quantum coherence has been established parallel with that of entanglement. In the resource theory, a resource can be well defined if given three ingredients: the free states, the resource, the (restricted) free operations. In this paper, we study the resource theory of coherence in a different light, that is, we consider the total coherence defined by the basis-free coherence maximized among all potential basis. We define the distillable total coherence and the total coherence cost and in both the asymptotic regime and the single-copy regime show the reversible transformation between a state with certain total coherence and the state with the unit reference total coherence. Extensively, we demonstrate that the total coherence can also be completely converted to the total correlation with the equal amount by the free operations. We also provide the alternative understanding of the total coherence, respectively, based on the entanglement and the total correlation in a different way.

  1. Further results on geometric operators in quantum gravity

    NARCIS (Netherlands)

    Loll, R.

    1996-01-01

    We investigate some properties of geometric operators in canonical quantum gravity in the connection approach `a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous discretized lattice quantities, compute various quantum

  2. Quantum information density scaling and qubit operation time constraints of CMOS silicon-based quantum computer architectures

    Science.gov (United States)

    Rotta, Davide; Sebastiano, Fabio; Charbon, Edoardo; Prati, Enrico

    2017-06-01

    Even the quantum simulation of an apparently simple molecule such as Fe2S2 requires a considerable number of qubits of the order of 106, while more complex molecules such as alanine (C3H7NO2) require about a hundred times more. In order to assess such a multimillion scale of identical qubits and control lines, the silicon platform seems to be one of the most indicated routes as it naturally provides, together with qubit functionalities, the capability of nanometric, serial, and industrial-quality fabrication. The scaling trend of microelectronic devices predicting that computing power would double every 2 years, known as Moore's law, according to the new slope set after the 32-nm node of 2009, suggests that the technology roadmap will achieve the 3-nm manufacturability limit proposed by Kelly around 2020. Today, circuital quantum information processing architectures are predicted to take advantage from the scalability ensured by silicon technology. However, the maximum amount of quantum information per unit surface that can be stored in silicon-based qubits and the consequent space constraints on qubit operations have never been addressed so far. This represents one of the key parameters toward the implementation of quantum error correction for fault-tolerant quantum information processing and its dependence on the features of the technology node. The maximum quantum information per unit surface virtually storable and controllable in the compact exchange-only silicon double quantum dot qubit architecture is expressed as a function of the complementary metal-oxide-semiconductor technology node, so the size scale optimizing both physical qubit operation time and quantum error correction requirements is assessed by reviewing the physical and technological constraints. According to the requirements imposed by the quantum error correction method and the constraints given by the typical strength of the exchange coupling, we determine the workable operation frequency

  3. Operational Markov Condition for Quantum Processes

    Science.gov (United States)

    Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan

    2018-01-01

    We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.

  4. Operational geometric phase for mixed quantum states

    International Nuclear Information System (INIS)

    Andersson, O; Heydari, H

    2013-01-01

    The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics. (paper)

  5. Quantum circuits cannot control unknown operations

    International Nuclear Information System (INIS)

    Araújo, Mateus; Feix, Adrien; Costa, Fabio; Brukner, Časlav

    2014-01-01

    One of the essential building blocks of classical computer programs is the ‘if’ clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation conditioned on the state of a control system. Here we show that this control cannot be performed by a quantum circuit if the unitary is completely unknown. The task remains impossible even if we allow the control to be done modulo a global phase. However, this no-go theorem does not prevent implementing quantum control of unknown unitaries in practice, as any physical implementation of an unknown unitary provides additional information that makes the control possible. We then argue that one should extend the quantum circuit formalism to capture this possibility in a straightforward way. This is done by allowing unknown unitaries to be applied to subspaces and not only to subsystems. (paper)

  6. Protected quantum computing: interleaving gate operations with dynamical decoupling sequences.

    Science.gov (United States)

    Zhang, Jingfu; Souza, Alexandre M; Brandao, Frederico Dias; Suter, Dieter

    2014-02-07

    Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2.

  7. Structural characterization and condition for measurement statistics preservation of a unital quantum operation

    International Nuclear Information System (INIS)

    Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H F

    2013-01-01

    We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states—a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on a finite-dimensional quantum state. (paper)

  8. Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system

    Science.gov (United States)

    Zhou, Nanrun; Chen, Weiwei; Yan, Xinyu; Wang, Yunqian

    2018-06-01

    In order to obtain higher encryption efficiency, a bit-level quantum color image encryption scheme by exploiting quantum cross-exchange operation and a 5D hyper-chaotic system is designed. Additionally, to enhance the scrambling effect, the quantum channel swapping operation is employed to swap the gray values of corresponding pixels. The proposed color image encryption algorithm has larger key space and higher security since the 5D hyper-chaotic system has more complex dynamic behavior, better randomness and unpredictability than those based on low-dimensional hyper-chaotic systems. Simulations and theoretical analyses demonstrate that the presented bit-level quantum color image encryption scheme outperforms its classical counterparts in efficiency and security.

  9. The effectiveness of quantum operations for eavesdropping on sealed messages

    International Nuclear Information System (INIS)

    Lopata, Paul A; Bahder, Thomas B

    2007-01-01

    A quantum protocol is described which enables a user to send sealed messages and that allows for the detection of active eavesdroppers. We examine a class of eavesdropping strategies, those that make use of quantum operations, and we determine the information gain versus disturbance caused by these strategies. We demonstrate this tradeoff with an example and we compare this protocol to quantum key distribution, quantum direct communication, and quantum seal protocols

  10. Quantum measurement with a positive operator-valued measure

    International Nuclear Information System (INIS)

    Brandt, Howard E

    2003-01-01

    In the quantum theory of measurement, the positive operator-valued measure (POVM) is an important concept, and its implementation can be useful. A POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and mention of the history of POVMs in quantum theory, a particular implementation of a POVM for use in the measurement of nonorthogonal photon polarization states is reviewed. The implementation consists simply of a Wollaston prism, a mirror, two beam splitters, a polarization rotator and three phototubes arranged in an interferometric configuration, and it is shown analytically that the device faithfully represents the POVM. Based on Neumark's extension theorem, the two-dimensional Hilbert space of the POVM implementation can be embedded in the three-dimensional Hilbert space of an ordinary projective-valued measure. Also, analytical expressions are given for the maximum Renyi information loss from the device to a disturbing probe, and for the error and inconclusive rates induced by the probe. Various aspects of the problem of probe optimization are elaborated

  11. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  12. Third-order differential ladder operators and supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Mateo, J; Negro, J

    2008-01-01

    Hierarchies of one-dimensional Hamiltonians in quantum mechanics admitting third-order differential ladder operators are studied. Each Hamiltonian has associated three-step Darboux (pseudo)-cycles and Painleve IV equations as a closure condition. The whole hierarchy is generated applying some operations on the cycles. These operations are investigated in the frame of supersymmetric quantum mechanics and mainly involve algebraic manipulations. A consistent geometric representation for the hierarchy and cycles is built that also helps in understanding the operations. Three kinds of hierarchies are distinguished and a realization based on the harmonic oscillator Hamiltonian is supplied, giving an interpretation for the spectral properties of the Hamiltonians of each hierarchy

  13. A Quantum Computational Semantics for Epistemic Logical Operators. Part I: Epistemic Structures

    Science.gov (United States)

    Beltrametti, Enrico; Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto; Sergioli, Giuseppe

    2014-10-01

    Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like "Alice knows that Bob does not understand that π is irrational" as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators ( to understand, to know…) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of "memorizing and retrieving information" can be formally represented, in this framework, by using a quantum teleportation phenomenon.

  14. Gain dynamics of quantum dot devices for dual-state operation

    Energy Technology Data Exchange (ETDEWEB)

    Kaptan, Y., E-mail: yuecel.kaptan@physik.tu-berlin.de; Herzog, B.; Kolarczik, M.; Owschimikow, N.; Woggon, U. [Institut für Optik und Atomare Physik, Technische Universität Berlin, Berlin (Germany); Schmeckebier, H.; Arsenijević, D.; Bimberg, D. [Institut für Festkörperphysik, Technische Universität Berlin, Berlin (Germany); Mikhelashvili, V.; Eisenstein, G. [Technion Institute of Technology, Faculty of Electrical Engineering, Haifa (Israel)

    2014-06-30

    Ground state gain dynamics of In(Ga)As-quantum dot excited state lasers are investigated via single-color ultrafast pump-probe spectroscopy below and above lasing threshold. Two-color pump-probe experiments are used to localize lasing and non-lasing quantum dots within the inhomogeneously broadened ground state. Single-color results yield similar gain recovery rates of the ground state for lasing and non-lasing quantum dots decreasing from 6 ps to 2 ps with increasing injection current. We find that ground state gain dynamics are influenced solely by the injection current and unaffected by laser operation of the excited state. This independence is promising for dual-state operation schemes in quantum dot based optoelectronic devices.

  15. Toward a new culture in verified quantum operations

    Science.gov (United States)

    Flammia, Steve

    Measuring error rates of quantum operations has become an indispensable component in any aspiring platform for quantum computation. As the quality of controlled quantum operations increases, the demands on the accuracy and precision with which we measure these error rates also grows. However, well-meaning scientists that report these error measures are faced with a sea of non-standardized methodologies and are often asked during publication for only coarse information about how their estimates were obtained. Moreover, there are serious incentives to use methodologies and measures that will continually produce numbers that improve with time to show progress. These problems will only get exacerbated as our typical error rates go from 1 in 100 to 1 in 1000 or less. This talk will survey existing challenges presented by the current paradigm and offer some suggestions for solutions than can help us move toward fair and standardized methods for error metrology in quantum computing experiments, and towards a culture that values full disclose of methodologies and higher standards for data analysis.

  16. Characterizations of fixed points of quantum operations

    International Nuclear Information System (INIS)

    Li Yuan

    2011-01-01

    Let φ A be a general quantum operation. An operator B is said to be a fixed point of φ A , if φ A (B)=B. In this note, we shall show conditions under which B, a fixed point φ A , implies that B is compatible with the operation element of φ A . In particular, we offer an extension of the generalized Lueders theorem.

  17. Operating single quantum emitters with a compact Stirling cryocooler.

    Science.gov (United States)

    Schlehahn, A; Krüger, L; Gschrey, M; Schulze, J-H; Rodt, S; Strittmatter, A; Heindel, T; Reitzenstein, S

    2015-01-01

    The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g((2))(0) Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g((2))(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.

  18. Operating single quantum emitters with a compact Stirling cryocooler

    Energy Technology Data Exchange (ETDEWEB)

    Schlehahn, A.; Krüger, L.; Gschrey, M.; Schulze, J.-H.; Rodt, S.; Strittmatter, A.; Heindel, T., E-mail: tobias.heindel@tu-berlin.de; Reitzenstein, S. [Institute of Solid State Physics, Technische Universität Berlin, 10623 Berlin (Germany)

    2015-01-15

    The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g{sup (2)}(0) < 0.04 from this Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g{sup (2)}(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.

  19. Lorentz-covariant reduced-density-operator theory for relativistic-quantum-information processing

    International Nuclear Information System (INIS)

    Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo

    2003-01-01

    In this paper, we derived a Lorentz-covariant quantum Liouville equation for the density operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced density operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics

  20. Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations

    Directory of Open Access Journals (Sweden)

    Jen-Tsung Hsiang

    2018-05-01

    Full Text Available Identifying or constructing a fine-grained microscopic theory that will emerge under specific conditions to a known macroscopic theory is always a formidable challenge. Thermodynamics is perhaps one of the most powerful theories and best understood examples of emergence in physical sciences, which can be used for understanding the characteristics and mechanisms of emergent processes, both in terms of emergent structures and the emergent laws governing the effective or collective variables. Viewing quantum mechanics as an emergent theory requires a better understanding of all this. In this work we aim at a very modest goal, not quantum mechanics as thermodynamics, not yet, but the thermodynamics of quantum systems, or quantum thermodynamics. We will show why even with this minimal demand, there are many new issues which need be addressed and new rules formulated. The thermodynamics of small quantum many-body systems strongly coupled to a heat bath at low temperatures with non-Markovian behavior contains elements, such as quantum coherence, correlations, entanglement and fluctuations, that are not well recognized in traditional thermodynamics, built on large systems vanishingly weakly coupled to a non-dynamical reservoir. For quantum thermodynamics at strong coupling, one needs to reexamine the meaning of the thermodynamic functions, the viability of the thermodynamic relations and the validity of the thermodynamic laws anew. After a brief motivation, this paper starts with a short overview of the quantum formulation based on Gelin & Thoss and Seifert. We then provide a quantum formulation of Jarzynski’s two representations. We show how to construct the operator thermodynamic potentials, the expectation values of which provide the familiar thermodynamic variables. Constructing the operator thermodynamic functions and verifying or modifying their relations is a necessary first step in the establishment of a viable thermodynamics theory for

  1. Lectures on algebraic quantum field theory and operator algebras

    International Nuclear Information System (INIS)

    Schroer, Bert

    2001-04-01

    In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)

  2. Double Tunneling Injection Quantum Dot Lasers for High Speed Operation

    Science.gov (United States)

    2017-10-23

    Double Tunneling-Injection Quantum Dot Lasers for High -Speed Operation The views, opinions and/or findings contained in this report are those of...SECURITY CLASSIFICATION OF: 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13. SUPPLEMENTARY NOTES 12. DISTRIBUTION AVAILIBILITY STATEMENT 6...State University Title: Double Tunneling-Injection Quantum Dot Lasers for High -Speed Operation Report Term: 0-Other Email: asryan@vt.edu Distribution

  3. Quantum operations that cannot be implemented using a small mixed environment

    International Nuclear Information System (INIS)

    Zalka, Christof; Rieffel, Eleanor

    2002-01-01

    To implement any quantum operation (a.k.a. ''superoperator'' or ''CP map'') on a d-dimensional quantum system, it is enough to apply a suitable overall unitary transformation to the system and a d 2 -dimensional environment which is initialized in a fixed pure state. It has been suggested that a d-dimensional environment might be enough if we could initialize the environment in a mixed state of our choosing. In this note we show with elementary means that certain explicit quantum operations cannot be realized in this way. Our counterexamples map some pure states to pure states, giving strong and easily manageable conditions on the overall unitary transformation. Everything works in the more general setting of quantum operations from d-dimensional to d ' -dimensional spaces, so we place our counterexamples within this more general framework

  4. Quantum maps from transfer operators

    International Nuclear Information System (INIS)

    Bogomolny, E.B.; Carioli, M.

    1992-09-01

    The Selberg zeta function ζ S (s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, ζ S (s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T s ), where T s is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T s . Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs

  5. Assessment of a quantum phase-gate operation based on nonlinear optics

    International Nuclear Information System (INIS)

    Rebic, S.; Ottaviani, C.; Di Giuseppe, G.; Vitali, D.; Tombesi, P.

    2006-01-01

    We analyze in detail the proposal for a two-qubit gate for travelling single-photon qubits recently presented by Ottaviani et al. [Phys. Rev. A 73, 010301(R) (2006)]. The scheme is based on an ensemble of five-level atoms coupled to two quantum and two classical light fields. The two quantum fields undergo cross-phase modulation induced by electromagnetically induced transparency. The performance of this two-qubit quantum phase gate for travelling single-photon qubits is thoroughly examined in the steady-state and transient regimes, by means of a full quantum treatment of the system dynamics. In the steady-state regime, we find a general trade-off between the size of the conditional phase shift and the fidelity of the gate operation. However, this trade-off can be bypassed in the transient regime, where a satisfactory gate operation is found to be possible, significantly reducing the gate operation time

  6. The operations of quantum logic gates with pure and mixed initial states.

    Science.gov (United States)

    Chen, Jun-Liang; Li, Che-Ming; Hwang, Chi-Chuan; Ho, Yi-Hui

    2011-04-07

    The implementations of quantum logic gates realized by the rovibrational states of a C(12)O(16) molecule in the X((1)Σ(+)) electronic ground state are investigated. Optimal laser fields are obtained by using the modified multitarget optimal theory (MTOCT) which combines the maxima of the cost functional and the fidelity for state and quantum process. The projection operator technique together with modified MTOCT is used to get optimal laser fields. If initial states of the quantum gate are pure states, states at target time approach well to ideal target states. However, if the initial states are mixed states, the target states do not approach well to ideal ones. The process fidelity is introduced to investigate the reliability of the quantum gate operation driven by the optimal laser field. We found that the quantum gates operate reliably whether the initial states are pure or mixed.

  7. Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels

    Science.gov (United States)

    Ruan, Liangzhong; Dai, Wenhan; Win, Moe Z.

    2018-05-01

    Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of the qubits to the other agent through a quantum channel. In this process, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. To address this challenge, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. This paper puts forth two recurrence QED algorithms that adapt to the quantum channel to tackle the efficiency issue. The proposed algorithms have guaranteed convergence for quantum channels with two Kraus operators, which include phase-damping and amplitude-damping channels. Analytical results show that the convergence speed of these algorithms is improved from linear to quadratic and one of the algorithms achieves the optimal speed. Numerical results confirm that the proposed algorithms significantly improve the efficiency of QED.

  8. Two-qubit logical operations in three quantum dots system.

    Science.gov (United States)

    Łuczak, Jakub; Bułka, Bogdan R

    2018-06-06

    We consider a model of two interacting always-on, exchange-only qubits for which controlled phase (CPHASE), controlled NOT (CNOT), quantum Fourier transform (QFT) and SWAP operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the CPHASE gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: CNOT, QFT and SWAP. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.

  9. Random operators disorder effects on quantum spectra and dynamics

    CERN Document Server

    Aizenman, Michael

    2015-01-01

    This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization-presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and rela...

  10. Numerical simulation of spin-qubit operation in coupled quantum dots

    International Nuclear Information System (INIS)

    Goto, Daisuke; Eto, Mikio

    2007-01-01

    Electronic states and spin operation in coupled quantum dots are numerically studied, considering realistic shape of quantum dots and electron-electron interaction. (i) We evaluate the spin coupling J between two electron spins, as a function of magnetic field perpendicular to the quantum dots. We observe a transition from antiferromagnetic coupling (J>0) to ferromagnetic coupling (J<0) at magnetic field of a few Tesla. The spin coupling is hardly influenced by the size difference between the quantum dots if the energy levels are matched. (ii) We simulate SWAP gate operations by calculating the time development of two electron spins. We show that a sudden change of tunnel barrier may result in the gate errors. The spin exchange is incomplete in the presence of strong spin-orbit interaction in InGaAs. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  11. Designing reversible arithmetic, logic circuit to implement micro-operation in quantum computation

    International Nuclear Information System (INIS)

    Kalita, Gunajit; Saikia, Navajit

    2016-01-01

    The futuristic computing is desired to be more power full with low-power consumption. That is why quantum computing has been a key area of research for quite some time and is getting more and more attention. Quantum logic being reversible, a significant amount of contributions has been reported on reversible logic in recent times. Reversible circuits are essential parts of quantum computers, and hence their designs are of great importance. In this paper, designs of reversible circuits are proposed using a recently proposed reversible gate for arithmetic and logic operations to implement various micro-operations (simple add and subtract, add with carry, subtract with borrow, transfer, incrementing, decrementing etc., and logic operations like XOR, XNOR, complementing etc.) in a reversible computer like quantum computer. The two new reversible designs proposed here for half adder and full adders are also used in the presented reversible circuits to implement various microoperations. The quantum costs of these designs are comparable. Many of the implemented micro-operations are not seen in previous literatures. The performances of the proposed circuits are compared with existing designs wherever available. (paper)

  12. Effective operator formalism for open quantum systems

    DEFF Research Database (Denmark)

    Reiter, Florentin; Sørensen, Anders Søndberg

    2012-01-01

    We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...... involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method...

  13. Eigenvalues of the volume operator in loop quantum gravity

    International Nuclear Information System (INIS)

    Meissner, Krzysztof A

    2006-01-01

    We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins, which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity

  14. Tight upper bound for the maximal quantum value of the Svetlichny operators

    Science.gov (United States)

    Li, Ming; Shen, Shuqian; Jing, Naihuan; Fei, Shao-Ming; Li-Jost, Xianqing

    2017-10-01

    It is a challenging task to detect genuine multipartite nonlocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequality (SI) for several quantum states, including the white and color noised Greenberger-Horne-Zeilinger (GHZ) states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation of GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.

  15. On the definition of time operator in quantum mechanics

    International Nuclear Information System (INIS)

    Nowicki, A.A.

    1974-01-01

    Different approaches to the quantum-mechanical definition of time operator T are briefly discussed. In particular we define the analytic continuation of the time operator and show that one can construct its exact eigenstates. We consider also the case of a relativistic free scalar particle and discuss the notion of proper time operator S. (author)

  16. Quantum logical states and operators for Josephson-like systems

    International Nuclear Information System (INIS)

    Faoro, Lara; Raffa, Francesco A; Rasetti, Mario

    2006-01-01

    We give a formal algebraic description of Josephson-type quantum dynamical systems, i.e., Hamiltonian systems with a cos θ-like potential term. The two-boson Heisenberg algebra plays for such systems the role that the h(1) algebra does for the harmonic oscillator. A single Josephson junction is selected as a representative of Josephson systems. We construct both logical states (codewords) and logical (gate) operators in the superconductive regime. The codewords are the even and odd coherent states of the two-boson algebra: they are shift-resistant and robust, due to squeezing. The logical operators acting on the qubit codewords are expressed in terms of operators in the enveloping of the two-boson algebra. Such a scheme appears to be relevant for quantum information applications. (letter to the editor)

  17. Quantum incompatibility of channels with general outcome operator algebras

    Science.gov (United States)

    Kuramochi, Yui

    2018-04-01

    A pair of quantum channels is said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input space and with general outcome operator algebras. We define a compatibility relation for such channels by identifying the composite outcome space as the maximal (projective) C*-tensor product of outcome algebras. We show theorems that characterize this compatibility relation in terms of the concatenation and conjugation of channels, generalizing the recent result for channels with quantum outcome spaces. These results are applied to the positive operator valued measures (POVMs) by identifying each of them with the corresponding quantum-classical (QC) channel. We also give a characterization of the maximality of a POVM with respect to the post-processing preorder in terms of the conjugate channel of the QC channel. We consider another definition of compatibility of normal channels by identifying the composite outcome space with the normal tensor product of the outcome von Neumann algebras. We prove that for a given normal channel, the class of normally compatible channels is upper bounded by a special class of channels called tensor conjugate channels. We show the inequivalence of the C*- and normal compatibility relations for QC channels, which originates from the possibility and impossibility of copying operations for commutative von Neumann algebras in C*- and normal compatibility relations, respectively.

  18. Quantum dynamics for classical systems with applications of the number operator

    CERN Document Server

    Bagarello, Fabio

    2013-01-01

    Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a uniqu...

  19. Quadratic Plus Linear Operators which Preserve Pure States of Quantum Systems: Small Dimensions

    International Nuclear Information System (INIS)

    Saburov, Mansoor

    2014-01-01

    A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system

  20. Quantum spacetime operationally based on propagators for extended test particles

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1981-01-01

    By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws of motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle

  1. An operator description of entanglement matching in quantum teleportation

    International Nuclear Information System (INIS)

    Kurucz, Z; Koniorczyk, M; Adam, P; Janszky, J

    2003-01-01

    The antilinear operator representation of bipartite pure states of the relative state formulation of quantum mechanics is applied to describe quantum teleportation schemes utilizing an arbitrary pure state as the entangled resource. Bennett type teleportation schemes with nonmaximally entangled pure states are characterized and the notion of 'entanglement matching' is introduced in general. Examples, including a scheme based on coherent-state superposition states of the electromagnetic field, are provided

  2. Operator algebras for general one-dimensional quantum mechanical potentials with discrete spectrum

    International Nuclear Information System (INIS)

    Wuensche, Alfred

    2002-01-01

    We define general lowering and raising operators of the eigenstates for one-dimensional quantum mechanical potential problems leading to discrete energy spectra and investigate their associative algebra. The Hamilton operator is quadratic in these lowering and raising operators and corresponding representations of operators for action and angle are found. The normally ordered representation of general operators using combinatorial elements such as partitions is derived. The introduction of generalized coherent states is discussed. Linear laws for the spacing of the energy eigenvalues lead to the Heisenberg-Weyl group and general quadratic laws of level spacing to unitary irreducible representations of the Lie group SU(1, 1) that is considered in detail together with a limiting transition from this group to the Heisenberg-Weyl group. The relation of the approach to quantum deformations is discussed. In two appendices, the classical and quantum mechanical treatment of the squared tangent potential is presented as a special case of a system with quadratic level spacing

  3. Operational Meanings of Orders of Observables Defined through Quantum Set Theories with Different Conditionals

    Directory of Open Access Journals (Sweden)

    Masanao Ozawa

    2017-01-01

    Full Text Available In quantum logic there is well-known arbitrariness in choosing a binary operation for conditional. Currently, we have at least three candidates, called the Sasaki conditional, the contrapositive Sasaki conditional, and the relevance conditional. A fundamental problem is to show how the form of the conditional follows from an analysis of operational concepts in quantum theory. Here, we attempt such an analysis through quantum set theory (QST. In this paper, we develop quantum set theory based on quantum logics with those three conditionals, each of which defines different quantum logical truth value assignment. We show that those three models satisfy the transfer principle of the same form to determine the quantum logical truth values of theorems of the ZFC set theory. We also show that the reals in the model and the truth values of their equality are the same for those models. Interestingly, however, the order relation between quantum reals significantly depends on the underlying conditionals. We characterize the operational meanings of those order relations in terms of joint probability obtained by the successive projective measurements of arbitrary two observables. Those characterizations clearly show their individual features and will play a fundamental role in future applications to quantum physics.

  4. Barrier versus tilt exchange gate operations in spin-based quantum computing

    Science.gov (United States)

    Shim, Yun-Pil; Tahan, Charles

    2018-04-01

    We present a theory for understanding the exchange interaction between electron spins in neighboring quantum dots, either by changing the detuning of the two quantum dots or independently tuning the tunneling barrier between quantum dots. The Hubbard model and a more realistic confining-potential model are used to investigate how the tilting and barrier control affect the effective exchange coupling and thus the gate fidelity in both the detuning and symmetric regimes. We show that the exchange coupling is less sensitive to the charge noise through tunnel barrier control (while allowing for exchange coupling operations on a sweet spot where the exchange interaction has zero derivative with respect to the detuning). Both GaAs and Si quantum dots are considered, and we compare our results with experimental data showing qualitative agreements. Our results answer the open question of why barrier gates are preferable to tilt gates for exchange-based gate operations.

  5. Quantum systems related to root systems and radial parts of Laplace operators

    OpenAIRE

    Olshanetsky, M. A.; Perelomov, A. M.

    2002-01-01

    The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.

  6. Relational motivation for conformal operator ordering in quantum cosmology

    International Nuclear Information System (INIS)

    Anderson, Edward

    2010-01-01

    Operator ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. This arises particularly naturally and simply from relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler-type actions for general relativity), for which all that is required is for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implement philosophical principles relevant to whole-universe modelling, so that the motivation for conformal operator ordering in quantum cosmology is thereby substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in various contexts. The conformal scaling of these actions directly tells us how emergent time scales; if one follows suit with the Newtonian time or the lapse in the more commonly used difference-type Euler-Lagrange or Arnowitt-Deser-Misner-type actions, one sees how these too obey a more complicated conformal invariance. Moreover, our discovery of the conformal scaling of the emergent time permits relating how this simplifies equations of motion with how affine parametrization simplifies geodesics.

  7. Qubits and quantum Hamiltonian computing performances for operating a digital Boolean 1/2-adder

    Science.gov (United States)

    Dridi, Ghassen; Faizy Namarvar, Omid; Joachim, Christian

    2018-04-01

    Quantum Boolean (1 + 1) digits 1/2-adders are designed with 3 qubits for the quantum computing (Qubits) and 4 quantum states for the quantum Hamiltonian computing (QHC) approaches. Detailed analytical solutions are provided to analyse the time operation of those different 1/2-adder gates. QHC is more robust to noise than Qubits and requires about the same amount of energy for running its 1/2-adder logical operations. QHC is faster in time than Qubits but its logical output measurement takes longer.

  8. Controlled Quantum Operations of a Semiconductor Three-Qubit System

    Science.gov (United States)

    Li, Hai-Ou; Cao, Gang; Yu, Guo-Dong; Xiao, Ming; Guo, Guang-Can; Jiang, Hong-Wen; Guo, Guo-Ping

    2018-02-01

    In a specially designed semiconductor device consisting of three capacitively coupled double quantum dots, we achieve strong and tunable coupling between a target qubit and two control qubits. We demonstrate how to completely switch on and off the target qubit's coherent rotations by presetting two control qubits' states. A Toffoli gate is, therefore, possible based on these control effects. This research paves a way for realizing full quantum-logic operations in semiconductor multiqubit systems.

  9. Investigating and improving student understanding of quantum mechanical observables and their corresponding operators in Dirac notation

    Science.gov (United States)

    Marshman, Emily; Singh, Chandralekha

    2018-01-01

    In quantum mechanics, for every physical observable, there is a corresponding Hermitian operator. According to the most common interpretation of quantum mechanics, measurement of an observable collapses the quantum state into one of the possible eigenstates of the operator and the corresponding eigenvalue is measured. Since Dirac notation is an elegant notation that is commonly used in upper-level quantum mechanics, it is important that students learn to express quantum operators corresponding to observables in Dirac notation in order to apply the quantum formalism effectively in diverse situations. Here we focus on an investigation that suggests that, even though Dirac notation is used extensively, many advanced undergraduate and PhD students in physics have difficulty expressing the identity operator and other Hermitian operators corresponding to physical observables in Dirac notation. We first describe the difficulties students have with expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We then discuss how the difficulties found via written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of these concepts. The QuILT strives to help students become proficient in expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We also discuss the effectiveness of the QuILT based on in-class evaluations.

  10. Random quantum operations

    International Nuclear Information System (INIS)

    Bruzda, Wojciech; Cappellini, Valerio; Sommers, Hans-Juergen; Zyczkowski, Karol

    2009-01-01

    We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Φ and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state

  11. BRST-operator for quantum Lie algebra and differential calculus on quantum groups

    International Nuclear Information System (INIS)

    Isaev, A.P.; Ogievetskij, O.V.

    2001-01-01

    For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru

  12. Irreducible normalizer operators and thresholds for degenerate quantum codes with sublinear distances

    Science.gov (United States)

    Pryadko, Leonid P.; Dumer, Ilya; Kovalev, Alexey A.

    2015-03-01

    We construct a lower (existence) bound for the threshold of scalable quantum computation which is applicable to all stabilizer codes, including degenerate quantum codes with sublinear distance scaling. The threshold is based on enumerating irreducible operators in the normalizer of the code, i.e., those that cannot be decomposed into a product of two such operators with non-overlapping support. For quantum LDPC codes with logarithmic or power-law distances, we get threshold values which are parametrically better than the existing analytical bound based on percolation. The new bound also gives a finite threshold when applied to other families of degenerate quantum codes, e.g., the concatenated codes. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.

  13. Quantifying non-classical and beyond-quantum correlations in the unified operator formalism

    International Nuclear Information System (INIS)

    Geller, Joshua; Piani, Marco

    2014-01-01

    Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond-quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels—that of operators and that of probability distributions—is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device-independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu–Rohrlich box. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’. (paper)

  14. The role of operator ordering in quantum field theory

    International Nuclear Information System (INIS)

    Suzuki, Tsuneo; Hirshfeld, A.C.; Leschke, H.

    1980-01-01

    We study the role of operator ordering in quantum field theory. Operator ordering techniques discussed in our previous papers in the quantum mechanical context are extended to field theory. In this case formally infinite terms appear which must be given a meaning in the framework of some definite regularization scheme. Different orderings for the non-commuting operators in the interaction Hamiltonian lead in general to different expressions for the Dyson-Wick expansion of the S-matrix, implying different Feynman rules. Different orderings correspond to different assignments for the initially undetermined values of the contractions occurring in closed-loop diagrams. Combining a special class of ordering schemes (u-ordering, a generalization of Weyl-ordering) with dimensional regularization leads to important simplifications, and in this case manipulations in which ordering complications are neglected may be justified. We use our methods to discuss gauge invariance in scalar electrodynamics, and the equivalent theorem for a reducible field theoretical model. (author)

  15. Quantum turnstile operation of single-molecule magnets

    International Nuclear Information System (INIS)

    Moldoveanu, V; Dinu, I V; Tanatar, B; Moca, C P

    2015-01-01

    The time-dependent transport through single-molecule magnets coupled to magnetic or non-magnetic electrodes is studied in the framework of the generalized master equation method. We investigate the transient regime induced by the periodic switching of the source and drain contacts. If the electrodes have opposite magnetizations the quantum turnstile operation allows the stepwise writing of intermediate excited states. In turn, the transient currents provide a way to read these states. Within our approach we take into account both the uniaxial and transverse anisotropy. The latter may induce additional quantum tunneling processes which affect the efficiency of the proposed read-and-write scheme. An equally weighted mixture of molecular spin states can be prepared if one of the electrodes is ferromagnetic. (paper)

  16. Geometrical aspects of operator ordering terms in gauge invariant quantum models

    International Nuclear Information System (INIS)

    Houston, P.J.

    1990-01-01

    Finite-dimensional quantum models with both boson and fermion degrees of freedom, and which have a gauge invariance, are studied here as simple versions of gauge invariant quantum field theories. The configuration space of these finite-dimensional models has the structure of a principal fibre bundle and has defined on it a metric which is invariant under the action of the bundle or gauge group. When the gauge-dependent degrees of freedom are removed, thereby defining the quantum models on the base of the principal fibre bundle, extra operator ordering terms arise. By making use of dimensional reduction methods in removing the gauge dependence, expressions are obtained here for the operator ordering terms which show clearly their dependence on the geometry of the principal fibre bundle structure. (author)

  17. Time Operator in Relativistic Quantum Mechanics

    Science.gov (United States)

    Khorasani, Sina

    2017-07-01

    It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

  18. Two-loop scale-invariant scalar potential and quantum effective operators

    CERN Document Server

    Ghilencea, D.M.

    2016-11-29

    Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...

  19. Conformal invariant quantum field theory and composite field operators

    International Nuclear Information System (INIS)

    Kurak, V.

    1976-01-01

    The present status of conformal invariance in quantum field theory is reviewed from a non group theoretical point of view. Composite field operators dimensions are computed in some simple models and related to conformal symmetry

  20. Field theoretical construction of an infinite set of quantum commuting operators related with soliton equations

    International Nuclear Information System (INIS)

    Sasaki, Ryu; Yamanaka, Itaru

    1987-01-01

    The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the ℎ → 0 limit (ℎ; Planck's constant divided by 2π). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie a certain class of quantum integrable systems. (orig.)

  1. Field theoretical construction of an infinite set of quantum commuting operators related with soliton equations

    International Nuclear Information System (INIS)

    Sasaki, Ryu; Yamanaka, Itaru.

    1986-08-01

    The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the ℎ → 0 limit (ℎ; Planck's constant divided by 2π). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie certain class of quantum integrable systems. (author)

  2. Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)

    2017-04-15

    To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)

  3. The q-difference operator, the quantum hyperplane, Hilbert spaces of analytic functions and q-oscillators

    International Nuclear Information System (INIS)

    Arik, M.

    1991-01-01

    It is shown that the differential calculus of Wess and Zumino for the quantum hyperplane is intimately related to the q-difference operator acting on the n-dimensional complex space C n . An explicit transformation relates the variables and the q-difference operators on C n to the variables and the quantum derivatives on the quantum hyperplane. For real values of the quantum parameter q, the consideration of the variables and the derivatives as hermitean conjugates yields a quantum deformation of the Bargmann-Segal Hilbert space of analytic functions on C n . Physically such a system can be interpreted as the quantum deformation of the n dimensional harmonic oscillator invariant under the unitary quantum group U q (n) with energy eigenvalues proportional to the basic integers. Finally, a construction of the variables and quantum derivatives on the quantum hyperplane in terms of variables and ordinary derivatives on C n is presented. (orig.)

  4. Global quantum discord and matrix product density operators

    Science.gov (United States)

    Huang, Hai-Lin; Cheng, Hong-Guang; Guo, Xiao; Zhang, Duo; Wu, Yuyin; Xu, Jian; Sun, Zhao-Yu

    2018-06-01

    In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called "discord density" can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.

  5. The SCOP-formalism: an Operational Approach to Quantum Mechanics

    International Nuclear Information System (INIS)

    D'Hooghe, Bart

    2010-01-01

    We present the SCOP-formalism, an operational approach to quantum mechanics. If a State-COntext-Property-System (SCOP) satisfies a specific set of 'quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.

  6. Foundations of quantum theory from classical concepts to operator algebras

    CERN Document Server

    Landsman, Klaas

    2017-01-01

    This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.

  7. Conal representation of quantum states and non-trace-preserving quantum operations

    International Nuclear Information System (INIS)

    Arrighi, Pablo; Patricot, Christophe

    2003-01-01

    We represent generalized density matrices of a d-complex dimensional quantum system as a subcone of a real pointed cone of revolution in R d 2 , or indeed a Minkowskian cone in E 1,d 2 -1 . Generalized pure states correspond to certain future-directed lightlike vectors of E 1,d 2 -1 . This extension of the generalized Bloch sphere enables us to cater for non-trace-preserving quantum operations, and in particular to view the per-outcome effects of generalized measurements. We show that these consist of the product of an orthogonal transform about the axis of the cone of revolution and a positive real linear transform. We give detailed formulas for the one-qubit case and express the post-measurement states in terms of the initial-state vectors and measurement vectors. We apply these results in order to find the information gain versus disturbance trade-off in the case of two equiprobable pure states. Thus we recover Fuchs and Peres's formula in an elegant manner

  8. The elliptic quantum algebra Uq,p(sl-hatN) and its vertex operators

    International Nuclear Information System (INIS)

    Chang Wenjing; Ding Xiangmao

    2009-01-01

    We construct a realization of the elliptic quantum algebra U q,p (sl-hat N ) for any given level k in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization of the quantum affine algebra U q (sl-hat N ). We also construct a family of screening currents, which commute with the currents of U q,p (sl-hat N ) up to total q-differences. And we give explicit twisted expressions for the type I and type II vertex operators of U q,p (sl-hat N ) by twisting the known results of the type I vertex operators of the quantum affine algebra U q (sl-hat N ) and the new results of the type II vertex operators of U q (sl-hat N ) we obtained in this paper.

  9. Some applicationS of non-Hermitian operators in quantum mechanics and quantum field theory

    International Nuclear Information System (INIS)

    Recami, E.; Rodrigues, W.A. Jr.; Smrz, P.

    1983-01-01

    Due to the possibility of rephrasing it in terms of Lie-admissible algebras, some work done in the past in collaboration with A., Agodi, M., Baldo and V.S., Olkhovsky is here reported. Such work led to the introduction of non-Hermitian operators in (classical and relativistic) quantum theory. In particular: (i) the association of unstable states (decaying 'Resonances') with the eigenvectors of non-Hermitian hamiltonians; (ii) the problem of the four position operators for relativistic spin-zero particles are dealth with

  10. The origin of the algebra of quantum operators in the stochastic formulation of quantum mechanics

    International Nuclear Information System (INIS)

    Davidson, M.

    1979-01-01

    The origin of the algebra of the non-commuting operators of quantum mechanics is explained in the general Fenyes-Nelson stochastic models in which the diffusion constant is a free parameter. This is achieved by continuing the diffusion constant to imaginary values, a continuation which destroys the physical interpretation, but does not affect experimental predictions. This continuation leads to great mathematical simplification in the stochastic theory, and to an understanding of the entire mathematical formalism of quantum mechanics. It is more than a formal construction because the diffusion parameter is not an observable in these theories. (Auth.)

  11. Antiunitary symmetry operators in quantum mechanics

    International Nuclear Information System (INIS)

    Carinena, J.F.; Santander, M.

    1981-01-01

    A criterion to decide that some symmetries of a quantum system must be realized as antiunitary operators is given. It is based on some mathematical theorems about the second cohomology group of the symmetry group when expressed in terms of those of a normal subgroup and the corresponding factor group. It is also shown that this criterion implies that the only possibility for the unitary subgroup in the Galilean case is that generated by the space reflection and the connected component containing the identity; otherwise only massless systems would arise. (author)

  12. Extended higher-spin superalgebras and their realizations in terms of quantum operators

    Energy Technology Data Exchange (ETDEWEB)

    Vasiliev, M A

    1988-01-01

    The realization of the N = 1 higher-spin superalgebra, proposed earlier by E.S. Fradkin and the author, is found in terms of bosonic quantum operators. The extended higher-spin superalgebras, generalizing ordinary extended supersymmetry with arbitrary N > 1, are constructed by adding fermion quantum operators. Automorphisms, real forms, subalgebras, contractions and invariant forms of these infinite-dimensional superalgebras are studied. The formulation of the higher-spin superalgebras is described in terms of symbols of operators by Berezin. We hope that this formulation will provide in future the powerful tool for constructing the complete solution of the higher-spin problem, the problem of introducing a consistent gravitational interaction for massless higher-spin fields (s > 2).

  13. Single-server blind quantum computation with quantum circuit model

    Science.gov (United States)

    Zhang, Xiaoqian; Weng, Jian; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing; Song, Tingting

    2018-06-01

    Blind quantum computation (BQC) enables the client, who has few quantum technologies, to delegate her quantum computation to a server, who has strong quantum computabilities and learns nothing about the client's quantum inputs, outputs and algorithms. In this article, we propose a single-server BQC protocol with quantum circuit model by replacing any quantum gate with the combination of rotation operators. The trap quantum circuits are introduced, together with the combination of rotation operators, such that the server is unknown about quantum algorithms. The client only needs to perform operations X and Z, while the server honestly performs rotation operators.

  14. Photonic quantum digital signatures operating over kilometer ranges in installed optical fiber

    Science.gov (United States)

    Collins, Robert J.; Fujiwara, Mikio; Amiri, Ryan; Honjo, Toshimori; Shimizu, Kaoru; Tamaki, Kiyoshi; Takeoka, Masahiro; Andersson, Erika; Buller, Gerald S.; Sasaki, Masahide

    2016-10-01

    The security of electronic communications is a topic that has gained noteworthy public interest in recent years. As a result, there is an increasing public recognition of the existence and importance of mathematically based approaches to digital security. Many of these implement digital signatures to ensure that a malicious party has not tampered with the message in transit, that a legitimate receiver can validate the identity of the signer and that messages are transferable. The security of most digital signature schemes relies on the assumed computational difficulty of solving certain mathematical problems. However, reports in the media have shown that certain implementations of such signature schemes are vulnerable to algorithmic breakthroughs and emerging quantum processing technologies. Indeed, even without quantum processors, the possibility remains that classical algorithmic breakthroughs will render these schemes insecure. There is ongoing research into information-theoretically secure signature schemes, where the security is guaranteed against an attacker with arbitrary computational resources. One such approach is quantum digital signatures. Quantum signature schemes can be made information-theoretically secure based on the laws of quantum mechanics while comparable classical protocols require additional resources such as anonymous broadcast and/or a trusted authority. Previously, most early demonstrations of quantum digital signatures required dedicated single-purpose hardware and operated over restricted ranges in a laboratory environment. Here, for the first time, we present a demonstration of quantum digital signatures conducted over several kilometers of installed optical fiber. The system reported here operates at a higher signature generation rate than previous fiber systems.

  15. Duality quantum algorithm efficiently simulates open quantum systems

    Science.gov (United States)

    Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu

    2016-01-01

    Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. PMID:27464855

  16. Toward demonstrating controlled-X operation based on continuous-variable four-partite cluster states and quantum teleporters

    International Nuclear Information System (INIS)

    Wang Yu; Su Xiaolong; Shen Heng; Tan Aihong; Xie Changde; Peng Kunchi

    2010-01-01

    One-way quantum computation based on measurement and multipartite cluster entanglement offers the ability to perform a variety of unitary operations only through different choices of measurement bases. Here we present an experimental study toward demonstrating the controlled-X operation, a two-mode gate in which continuous variable (CV) four-partite cluster states of optical modes are utilized. Two quantum teleportation elements are used for achieving the gate operation of the quantum state transformation from input target and control states to output states. By means of the optical cluster state prepared off-line, the homodyne detection and electronic feeding forward, the information carried by the input control state is transformed to the output target state. The presented scheme of the controlled-X operation based on teleportation can be implemented nonlocally and deterministically. The distortion of the quantum information resulting from the imperfect cluster entanglement is estimated with the fidelity.

  17. Automated quantum operations in photonic qutrits

    Science.gov (United States)

    Borges, G. F.; Baldijão, R. D.; Condé, J. G. L.; Cabral, J. S.; Marques, B.; Terra Cunha, M.; Cabello, A.; Pádua, S.

    2018-02-01

    We report an experimental implementation of automated state transformations on spatial photonic qutrits following the theoretical proposal made by Baldijão et al. [Phys. Rev. A 96, 032329 (2017), 10.1103/PhysRevA.96.032329]. A qutrit state is simulated by using three Gaussian beams, and after some state operations, the transformed state is available in the end in terms of the basis state. The state transformation setup uses a spatial light modulator and a calcite-based interferometer. The results reveal the usefulness of the operation method. The experimental data show a good agreement with theoretical predictions, opening possibilities for explorations in higher dimensions and in a wide range of applications. This is a necessary step in qualifying spatial photonic qudits as a competitive setup for experimental research in the implementation of quantum algorithms which demand a large number of steps.

  18. ABC of ladder operators for rationally extended quantum harmonic oscillator systems

    Science.gov (United States)

    Cariñena, José F.; Plyushchay, Mikhail S.

    2017-07-01

    The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.

  19. Norm estimates of complex symmetric operators applied to quantum systems

    International Nuclear Information System (INIS)

    Prodan, Emil; Garcia, Stephan R; Putinar, Mihai

    2006-01-01

    This paper communicates recent results in the theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schroedinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schroedinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schroedinger operators appearing in the complex scaling theory of resonances

  20. Density functional representation of quantum chemistry. II. Local quantum field theories of molecular matter in terms of the charge density operator do not work

    International Nuclear Information System (INIS)

    Primas, H.; Schleicher, M.

    1975-01-01

    A comprehensive review of the attempts to rephrase molecular quantum mechanics in terms of the particle density operator and the current density or phase density operator is given. All pertinent investigations which have come to attention suffer from severe mathematical inconsistencies and are not adequate to the few-body problem of quantum chemistry. The origin of the failure of these attempts is investigated, and it is shown that a realization of a local quantum field theory of molecular matter in terms of observables would presuppose the solution of many highly nontrivial mathematical problems

  1. Extended SUSY quantum mechanics, intertwining operators and coherent states

    International Nuclear Information System (INIS)

    Bagarello, F.

    2008-01-01

    We propose an extension of supersymmetric quantum mechanics which produces a family of isospectral Hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau-Klauder type associated to our Hamiltonians

  2. Bessel equation as an operator identity's matrix element in quantum mechanics

    International Nuclear Information System (INIS)

    Fan Hongyi; Li Chao

    2004-01-01

    We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented

  3. Quantum symmetry in quantum theory

    International Nuclear Information System (INIS)

    Schomerus, V.

    1993-02-01

    Symmetry concepts have always been of great importance for physical problems like explicit calculations, classification or model building. More recently, new 'quantum symmetries' ((quasi) quantum groups) attracted much interest in quantum theory. It is shown that all these quantum symmetries permit a conventional formulation as symmetry in quantum mechanics. Symmetry transformations can act on the Hilbert space H of physical states such that the ground state is invariant and field operators transform covariantly. Models show that one must allow for 'truncation' in the tensor product of representations of a quantum symmetry. This means that the dimension of the tensor product of two representations of dimension σ 1 and σ 2 may be strictly smaller than σ 1 σ 2 . Consistency of the transformation law of field operators local braid relations leads us to expect, that (weak) quasi quantum groups are the most general symmetries in local quantum theory. The elements of the R-matrix which appears in these local braid relations turn out to be operators on H in general. It will be explained in detail how examples of field algebras with weak quasi quantum group symmetry can be obtained. Given a set of observable field with a finite number of superselection sectors, a quantum symmetry together with a complete set of covariant field operators which obey local braid relations are constructed. A covariant transformation law for adjoint fields is not automatic but will follow when the existence of an appropriate antipode is assumed. At the example of the chiral critical Ising model, non-uniqueness of the quantum symmetry will be demonstrated. Generalized quantum symmetries yield examples of gauge symmetries in non-commutative geometry. Quasi-quantum planes are introduced as the simplest examples of quasi-associative differential geometry. (Weak) quasi quantum groups can act on them by generalized derivations much as quantum groups do in non-commutative (differential-) geometry

  4. Nanophotonic quantum computer based on atomic quantum transistor

    International Nuclear Information System (INIS)

    Andrianov, S N; Moiseev, S A

    2015-01-01

    We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks. (quantum computations)

  5. Nanophotonic quantum computer based on atomic quantum transistor

    Energy Technology Data Exchange (ETDEWEB)

    Andrianov, S N [Institute of Advanced Research, Academy of Sciences of the Republic of Tatarstan, Kazan (Russian Federation); Moiseev, S A [Kazan E. K. Zavoisky Physical-Technical Institute, Kazan Scientific Center, Russian Academy of Sciences, Kazan (Russian Federation)

    2015-10-31

    We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks. (quantum computations)

  6. Modeling of electrical and mesoscopic circuits at quantum nanoscale from heat momentum operator

    Science.gov (United States)

    El-Nabulsi, Rami Ahmad

    2018-04-01

    We develop a new method to study electrical circuits at quantum nanoscale by introducing a heat momentum operator which reproduces quantum effects similar to those obtained in Suykens's nonlocal-in-time kinetic energy approach for the case of reversible motion. The series expansion of the heat momentum operator is similar to the momentum operator obtained in the framework of minimal length phenomenologies characterized by the deformation of Heisenberg algebra. The quantization of both LC and mesoscopic circuits revealed a number of motivating features like the emergence of a generalized uncertainty relation and a minimal charge similar to those obtained in the framework of minimal length theories. Additional features were obtained and discussed accordingly.

  7. Fractional quantum integral operator with general kernels and applications

    Science.gov (United States)

    Babakhani, Azizollah; Neamaty, Abdolali; Yadollahzadeh, Milad; Agahi, Hamzeh

    In this paper, we first introduce the concept of fractional quantum integral with general kernels, which generalizes several types of fractional integrals known from the literature. Then we give more general versions of some integral inequalities for this operator, thus generalizing some previous results obtained by many researchers.2,8,25,29,30,36

  8. Operators and representation theory canonical models for algebras of operators arising in quantum mechanics

    CERN Document Server

    Jorgensen, Palle E T

    1987-01-01

    Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e

  9. Efficient quantum repeater with respect to both entanglement-concentration rate and complexity of local operations and classical communication

    Science.gov (United States)

    Su, Zhaofeng; Guan, Ji; Li, Lvzhou

    2018-01-01

    Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, in practice, it is difficult to distribute quantum entanglement over a long distance, due to the absorption and noise in quantum channels. A solution to this challenge is a quantum repeater, which can extend the distance of entanglement distribution. In this scheme, the time consumption of classical communication and local operations takes an important place with respect to time efficiency. Motivated by this observation, we consider a basic quantum repeater scheme that focuses on not only the optimal rate of entanglement concentration but also the complexity of local operations and classical communication. First, we consider the case where two different two-qubit pure states are initially distributed in the scenario. We construct a protocol with the optimal entanglement-concentration rate and less consumption of local operations and classical communication. We also find a criterion for the projective measurements to achieve the optimal probability of creating a maximally entangled state between the two ends. Second, we consider the case in which two general pure states are prepared and general measurements are allowed. We get an upper bound on the probability for a successful measurement operation to produce a maximally entangled state without any further local operations.

  10. Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado

    1997-10-01

    The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.

  11. Deterministic Quantum Secure Direct Communication with Dense Coding and Continuous Variable Operations

    International Nuclear Information System (INIS)

    Han Lianfang; Chen Yueming; Yuan Hao

    2009-01-01

    We propose a deterministic quantum secure direct communication protocol by using dense coding. The two check photon sequences are used to check the securities of the channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthermore, this protocol has the advantage of high capacity and can be realized in the experiment. (general)

  12. Duality Quantum Information and Duality Quantum Communication

    International Nuclear Information System (INIS)

    Li, C. Y.; Wang, W. Y.; Wang, C.; Song, S. Y.; Long, G. L.

    2011-01-01

    Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called duality quantum computing mode. The quantum particle-wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.

  13. Quantum thermodynamics of general quantum processes.

    Science.gov (United States)

    Binder, Felix; Vinjanampathy, Sai; Modi, Kavan; Goold, John

    2015-03-01

    Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorizes the output state. Moreover, the change in entropy is also positive for the same majorization condition. This makes a strong connection between the two operational laws of thermodynamics.

  14. Quantum space and quantum completeness

    Science.gov (United States)

    Jurić, Tajron

    2018-05-01

    Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

  15. Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory

    International Nuclear Information System (INIS)

    Klymenko, M. V.; Klein, M.; Levine, R. D.; Remacle, F.

    2016-01-01

    A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.

  16. Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory

    Energy Technology Data Exchange (ETDEWEB)

    Klymenko, M. V. [Department of Chemistry, University of Liège, B4000 Liège (Belgium); Klein, M. [The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Levine, R. D. [The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Crump Institute for Molecular Imaging and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine and Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095 (United States); Remacle, F., E-mail: fremacle@ulg.ac.be [Department of Chemistry, University of Liège, B4000 Liège (Belgium); The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)

    2016-07-14

    A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.

  17. Invariant class operators in the decoherent histories analysis of timeless quantum theories

    International Nuclear Information System (INIS)

    Halliwell, J. J.; Wallden, P.

    2006-01-01

    The decoherent histories approach to quantum theory is applied to a class of reparametrization-invariant models whose state is an energy eigenstate. A key step in this approach is the construction of class operators characterizing the questions of physical interest, such as the probability of the system entering a given region of configuration space without regard to time. In nonrelativistic quantum mechanics these class operators are given by time-ordered products of projection operators. But in reparametrization-invariant models, where there is no time, the construction of the class operators is more complicated, the main difficulty being to find operators which commute with the Hamiltonian constraint (and so respect the invariance of the theory). Here, inspired by classical considerations, we put forward a proposal for the construction of such class operators for a class of reparametrization-invariant systems. They consist of continuous infinite temporal products of Heisenberg picture projection operators. We investigate the consequences of this proposal in a number of simple models and also compare with the evolving constants method. The formalism developed here is ultimately aimed at cosmological models described by a Wheeler-DeWitt equation, but the specific features of such models are left to future papers

  18. Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

    Science.gov (United States)

    Wu, Yinghua; Herman, Michael F.; Batista, Victor S.

    2005-03-01

    A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit/split-operator Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP/SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.

  19. Quantum Computation and Quantum Spin Dynamics

    NARCIS (Netherlands)

    Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji

    2001-01-01

    We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum

  20. Combined and controlled remote implementations of partially unknown quantum operations of multiqubits using Greenberger-Horne-Zeilinger states

    International Nuclear Information System (INIS)

    Wang Anmin

    2007-01-01

    We propose and prove protocols of combined and controlled remote implementations of partially unknown quantum operations belonging to the restricted sets [A. M. Wang, Phys. Rev. A 74, 032317 (2006)] using Greenberger-Horne-Zeilinger (GHZ) states. We present the protocols in detail in the cases of one qubit, with two senders and with one controller, respectively. Then we study the variations of protocols with many senders, or with many controllers, or with both many senders and controllers using a multipartite GHZ state. Furthermore, we extend these protocols to the cases of multiqubits. Because our protocols have to request that the senders work together and transfer the information in turn or receive the repertoire of extra supercontrollers, or/and the controller(s) open the quantum channel and distribute the passwords in different ways, they definitely have the strong security in remote quantum information processing and communications. Moreover, the combined protocol with many senders is helpful to arrive at the power of remote implementations of quantum operations to the utmost extent in theory, since the different senders may have different operational resources and different operational rights in practice, and the controlled protocol with many controllers is able to enhance security and increase applications of remote implementations of quantum operations in engineering, since it has some common features in a controlled process

  1. Perturbation theory of low-dimensional quantum liquids. I. The pseudoparticle-operator basis

    International Nuclear Information System (INIS)

    Carmelo, J.M.P.; Castro Neto, A.H.; Campbell, D.K.

    1994-01-01

    We introduce an operator algebra for the description of the low-energy physics of one-dimensional, integrable, multicomponent quantum liquids. Considering the particular case of the Hubbard chain in a magnetic field and chemical potential, we show that at low energy its Bethe-ansatz solution can be interpreted in terms of a pseudoparticle-operator algebra. Our algebraic approach provides a concise interpretation of, and justification for, several recent studies of low-energy excitations and trasnport which have been based on detailed analyses of specific Bethe-ansatz eigenfunctions and eigenenergies. A central point is that the exact ground state of the interacting many-electron problem is the noninteracting pseudoparticle ground state. Furthermore, in the pseudoparticle basis, the quantum problem becomes perturbative, i.e., the two-pseudoparticle forward-scattering vertices and amplitudes do not diverge, and one can define a many-pseudoparticle perturbation theory. We write the general quantum-liquid Hamiltonian in the pseudoparticle basis and show that the pseudoparticle-perturbation theory leads, in a natural way, to the generalized Landau-liquid approach

  2. Interpreting quantum discord through quantum state merging

    International Nuclear Information System (INIS)

    Madhok, Vaibhav; Datta, Animesh

    2011-01-01

    We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. Our interpretation has an intuitive explanation based on the strong subadditivity of von Neumann entropy. We use our result to provide operational interpretations of other quantities like the local purity and quantum deficit. Finally, we discuss in brief some instances where our interpretation is valid in the single-copy scenario.

  3. Structure of Pioncare covariant tensor operators in quantum mechanical models

    International Nuclear Information System (INIS)

    Polyzou, W.N.; Klink, W.H.

    1988-01-01

    The structure of operators that transform covariantly in Poincare invariant quantum mechanical models is analyzed. These operators are shown to have an interaction dependence that comes from the geometry of the Poincare group. The operators can be expressed in terms of matrix elements in a complete set of eigenstates of the mass and spin operators associated with the dynamical representation of the Poincare group. The matrix elements are factored into geometrical coefficients (Clebsch--Gordan coefficients for the Poincare group) and invariant matrix elements. The geometrical coefficients are fixed by the transformation properties of the operator and the eigenvalue spectrum of the mass and spin. The invariant matrix elements, which distinguish between different operators with the same transformation properties, are given in terms of a set of invariant form factors. copyright 1988 Academic Press, Inc

  4. On the discrete spectrum of the Dirac operator on bent chain quantum graph

    Directory of Open Access Journals (Sweden)

    Belov Michail

    2017-01-01

    Full Text Available We study Dirac operators on an infinite quantum graph of a bent chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter α ∈ ℝ. We are interested in the discrete spectrum of the corresponding Hamiltonian. It can be non-empty due to a local (geometrical perturbation of the corresponding infinite chain of rings. The quantum graph of analogous geometry with the Schrodinger operator on the edges was considered by Duclos, Exner and Turek in 2008. They showed that the absence of δ-couplings at vertices (i.e. the Kirchhoff condition at the vertices lead to the absence of eigenvalues. We consider the relativistic particle (the Dirac operator instead of the Schrodinger one but the result is analogous. Quantum graphs of such type are suitable for description of grapheme-based nanostructures. It is established that the negativity of α is the necessary and sufficient condition for the existence of eigenvalues of the Dirac operator (i.e. the discrete spectrum of the Hamiltonian in this case is not empty. The continuous spectrum of the Hamiltonian for bent chain graph coincides with that for the corresponding straight infinite chain. Conditions for appearance of more than one eigenvalue are obtained. It is related to the bending angle. The investigation is based on the transfer-matrix approach. It allows one to reduce the problem to an algebraic task. δ-couplings was introduced by the operator extensions theory method.

  5. A quantum particle swarm optimizer with chaotic mutation operator

    International Nuclear Information System (INIS)

    Coelho, Leandro dos Santos

    2008-01-01

    Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm that shares many similarities with evolutionary computation techniques. However, the PSO is driven by the simulation of a social psychological metaphor motivated by collective behaviors of bird and other social organisms instead of the survival of the fittest individual. Inspired by the classical PSO method and quantum mechanics theories, this work presents a novel Quantum-behaved PSO (QPSO) using chaotic mutation operator. The application of chaotic sequences based on chaotic Zaslavskii map instead of random sequences in QPSO is a powerful strategy to diversify the QPSO population and improve the QPSO's performance in preventing premature convergence to local minima. The simulation results demonstrate good performance of the QPSO in solving a well-studied continuous optimization problem of mechanical engineering design

  6. Covariance operator of functional measure in P(φ)2-quantum field theory

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; Zhidkov, E.P.

    1988-01-01

    Functional integration measure in the Euclidean quantum field theory with polynomial interactions of boson fields with zero spin in two-dimensional space-time is investigated. The representation for the kernal of the measure covariance operator is obtained in the form of expansion over the eigenfunctions of some boundary problem for the heat equation. Two cases of the integration domains with different configurations are considered. Some trends and perspectives of employing the functional integration method in quantum field theory are also discussed. 43 refs

  7. Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations

    International Nuclear Information System (INIS)

    Roga, W; Illuminati, F; Spehner, D

    2016-01-01

    We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking. (paper)

  8. Characterizing and quantifying quantum chaos with quantum ...

    Indian Academy of Sciences (India)

    We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal ...

  9. Preparation of freezing quantum state for quantum coherence

    Science.gov (United States)

    Yang, Lian-Wu; Man, Zhong-Xiao; Zhang, Ying-Jie; Han, Feng; Du, Shao-jiang; Xia, Yun-Jie

    2018-06-01

    We provide a method to prepare the freezing quantum state for quantum coherence via unitary operations. The initial product state consists of the control qubit and target qubit; when it satisfies certain conditions, the initial product state converts into the particular Bell diagonal state under the unitary operations, which have the property of freezing of quantum coherence under quantum channels. We calculate the frozen quantum coherence and corresponding quantum correlations, and find that the quantities are determined by the control qubit only when the freezing phenomena occur.

  10. Quantum stochastic calculus associated with quadratic quantum noises

    International Nuclear Information System (INIS)

    Ji, Un Cig; Sinha, Kalyan B.

    2016-01-01

    We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus

  11. Quantum stochastic calculus associated with quadratic quantum noises

    Energy Technology Data Exchange (ETDEWEB)

    Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)

    2016-02-15

    We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

  12. Quantum ballistic evolution in quantum mechanics: Application to quantum computers

    International Nuclear Information System (INIS)

    Benioff, P.

    1996-01-01

    Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proven that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics. Also the definition of quantum Turing machines used here is compared with that used by other authors. copyright 1996 The American Physical Society

  13. The measurement problem in quantum mechanics: approximation to the phenomenon of decoherence by operational identities

    International Nuclear Information System (INIS)

    Usera, J.I.

    1996-01-01

    An approach based on bits and pieces of standard wisdom plus and operational quantum mechanical identity deduced by the author is presented here in order to convey arguments concerning the quantum theory of measurement and which betray a flavor against completive claims for quantum mechanics. Special emphasis is put on the phenomenon of decoherence. This phenomenon (which is experimentally verifiable) finds natural room within the formalism while the wave function collapse (which is not) is precluded. (Author)

  14. Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations

    International Nuclear Information System (INIS)

    Xiao, Y-F; Gao, J; McMillan, J F; Yang, X; Wong, C W; Zou, X-B; Chen, Y-L; Han, Z-F; Guo, G-C

    2008-01-01

    In this paper, a scalable photonic crystal cavity array, in which single embedded quantum dots (QDs) are coherently interacting, is studied theoretically. Firstly, we examine the spectral character and optical delay brought about by the coupled cavities interacting with single QDs, in an optical analogue to electromagnetically induced transparency. Secondly, we then examine the usability of this coupled QD-cavity system for quantum phase gate operation and our numerical examples suggest that a two-qubit system with fidelity above 0.99 and photon loss below 0.04 is possible.

  15. Emergent mechanics, quantum and un-quantum

    Science.gov (United States)

    Ralston, John P.

    2013-10-01

    There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications

  16. The elliptic quantum algebra U{sub q,p}(sl-hat{sub N}) and its vertex operators

    Energy Technology Data Exchange (ETDEWEB)

    Chang Wenjing [School of Mathematical Science, Capital Normal University, Beijing 100048 (China); Ding Xiangmao [Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)], E-mail: wjchang@amss.ac.cn, E-mail: xmding@amss.ac.cn

    2009-10-23

    We construct a realization of the elliptic quantum algebra U{sub q,p}(sl-hat{sub N}) for any given level k in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization of the quantum affine algebra U{sub q}(sl-hat{sub N}). We also construct a family of screening currents, which commute with the currents of U{sub q,p}(sl-hat{sub N}) up to total q-differences. And we give explicit twisted expressions for the type I and type II vertex operators of U{sub q,p}(sl-hat{sub N}) by twisting the known results of the type I vertex operators of the quantum affine algebra U{sub q}(sl-hat{sub N}) and the new results of the type II vertex operators of U{sub q}(sl-hat{sub N}) we obtained in this paper.

  17. Distinct Lasing Operation From Chirped InAs/InP Quantum-Dash Laser

    KAUST Repository

    Khan, Mohammed Zahed Mustafa; Ng, Tien Khee; Lee, Chi-Sen; Anjum, Dalaver H.; Cha, Dong Kyu; Bhattacharya, Pallab K.; Ooi, Boon S.

    2013-01-01

    We study the enhanced inhomogeneity across the InAs quantum-dash (Qdash) layers by incorporating a chirped AlGaInAs barrier thickness in the InAs/InP laser structure. The lasing operation is investigated via Fabry-Pérot ridge-waveguide laser

  18. XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

    Science.gov (United States)

    Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.

    2018-01-01

    Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

  19. Quantum operation for a one-qubit system under a non-Markovian environment

    International Nuclear Information System (INIS)

    Xue Shibei; Zhang Jing; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

    2011-01-01

    This paper introduces a simple alternating-current (AC) control strategy to perform quantum state manipulations under non-Markovian noise. A genetic algorithm is adopted to optimize the parameters of the AC control, which can be further used to fulfil one-qubit quantum operations at a given final time. Theoretical analysis and simulations show that our method works almost equally well for 1/f noise, ohmic, sub-ohmic and super-ohmic noise, which demonstrates the robustness of our strategy for noise with various spectra. In comparison with the Markovian cases, our method is more suitable to be used to suppress non-Markovian noise.

  20. Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

    Science.gov (United States)

    Miller, W., Jr.; Li, Q.

    2015-04-01

    The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

  1. Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

    International Nuclear Information System (INIS)

    Miller, W Jr; Li, Q

    2015-01-01

    The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L 2 of H in terms of an eigenbasis of another symmetry operator L 1 , but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions. (paper)

  2. Quantum computers and quantum computations

    International Nuclear Information System (INIS)

    Valiev, Kamil' A

    2005-01-01

    This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review. (reviews of topical problems)

  3. Quantum theory of measurements as quantum decision theory

    International Nuclear Information System (INIS)

    Yukalov, V I; Sornette, D

    2015-01-01

    Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device

  4. Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators

    Science.gov (United States)

    Niu, Murphy Yuezhen; Chuang, Isaac L.; Shapiro, Jeffrey H.

    2018-03-01

    We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ(2 )-interaction based quantum computation in multimode Fock bases: the χ(2 ) parity-check code, the χ(2 ) embedded error-correcting code, and the χ(2 ) binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via χ(2 ) Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The χ(2 ) binomial code is of special interest because, with m ≤N identified from channel monitoring, it can correct m -photon-loss errors, or m -photon-gain errors, or (m -1 )th -order dephasing errors using logical qudits that are encoded in O (N ) photons. In comparison, other bosonic QEC codes require O (N2) photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ(2 ) parity-check code and the χ(2 ) embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our χ(2 ) QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.

  5. Remote one-qubit information concentration and decoding of operator quantum error-correction codes

    International Nuclear Information System (INIS)

    Hsu Liyi

    2007-01-01

    We propose the general scheme of remote one-qubit information concentration. To achieve the task, the Bell-correlated mixed states are exploited. In addition, the nonremote one-qubit information concentration is equivalent to the decoding of the quantum error-correction code. Here we propose how to decode the stabilizer codes. In particular, the proposed scheme can be used for the operator quantum error-correction codes. The encoded state can be recreated on the errorless qubit, regardless how many bit-flip errors and phase-flip errors have occurred

  6. Unknown quantum states: The quantum de Finetti representation

    International Nuclear Information System (INIS)

    Caves, Carlton M.; Fuchs, Christopher A.; Schack, Ruediger

    2002-01-01

    We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an ''unknown quantum state'' in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point

  7. Application of Blind Quantum Computation to Two-Party Quantum Computation

    Science.gov (United States)

    Sun, Zhiyuan; Li, Qin; Yu, Fang; Chan, Wai Hong

    2018-03-01

    Blind quantum computation (BQC) allows a client who has only limited quantum power to achieve quantum computation with the help of a remote quantum server and still keep the client's input, output, and algorithm private. Recently, Kashefi and Wallden extended BQC to achieve two-party quantum computation which allows two parties Alice and Bob to perform a joint unitary transform upon their inputs. However, in their protocol Alice has to prepare rotated single qubits and perform Pauli operations, and Bob needs to have a powerful quantum computer. In this work, we also utilize the idea of BQC to put forward an improved two-party quantum computation protocol in which the operations of both Alice and Bob are simplified since Alice only needs to apply Pauli operations and Bob is just required to prepare and encrypt his input qubits.

  8. Application of Blind Quantum Computation to Two-Party Quantum Computation

    Science.gov (United States)

    Sun, Zhiyuan; Li, Qin; Yu, Fang; Chan, Wai Hong

    2018-06-01

    Blind quantum computation (BQC) allows a client who has only limited quantum power to achieve quantum computation with the help of a remote quantum server and still keep the client's input, output, and algorithm private. Recently, Kashefi and Wallden extended BQC to achieve two-party quantum computation which allows two parties Alice and Bob to perform a joint unitary transform upon their inputs. However, in their protocol Alice has to prepare rotated single qubits and perform Pauli operations, and Bob needs to have a powerful quantum computer. In this work, we also utilize the idea of BQC to put forward an improved two-party quantum computation protocol in which the operations of both Alice and Bob are simplified since Alice only needs to apply Pauli operations and Bob is just required to prepare and encrypt his input qubits.

  9. Stability of Quantum Loops and Exchange Operations in the Construction of Quantum Computation Gates

    International Nuclear Information System (INIS)

    Bermúdez, D; Delgado, F

    2017-01-01

    Quantum information and quantum computation is a rapidly emergent field where quantum systems and their applications play a central role. In the gate version of quantum computation, the construction of universal quantum gates to manipulate quantum information is currently an intensive arena for quantum engineering. Specific properties of systems should be able to reproduce such idealized gates imitating the classically inspired computational gates. Recently, for magnetic systems driven by the bipartite Heisenberg-Ising model a universal set of gates has been realized, an alternative easy design for the Boykin set but using the Bell states as grammar. Exact control can be then used to construct specific prescriptions to achieve those gates. Physical parameters impose a challenge in the gate control. This work analyzes, based on the worst case quantum fidelity, the associated instability for the proposed set of gates. An strong performance is found in those gates for the most of quantum states involved. (paper)

  10. The tree technique and irreducible tensor operators for the quantum algebra suq (2). The algebra of irreducible tensor operators

    International Nuclear Information System (INIS)

    Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.

    1993-01-01

    The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs

  11. Quantum games as quantum types

    Science.gov (United States)

    Delbecque, Yannick

    In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other

  12. Classical optics representation of the quantum mechanical translation operator via ABCD matrices

    International Nuclear Information System (INIS)

    Ornigotti, Marco; Aiello, Andrea

    2013-01-01

    The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established. (paper)

  13. Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

    International Nuclear Information System (INIS)

    Rabinovich, Vladimir S; Roch, Steffen

    2009-01-01

    This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z n which are discrete analogs of the Schroedinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of pseudodifference operators (i.e., pseudodifferential operators on the group Z n with analytic symbols), and the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schroedinger operators on Z n , Dirac operators on Z 3 and square root Klein-Gordon operators on Z n .

  14. Efficient universal quantum channel simulation in IBM's cloud quantum computer

    Science.gov (United States)

    Wei, Shi-Jie; Xin, Tao; Long, Gui-Lu

    2018-07-01

    The study of quantum channels is an important field and promises a wide range of applications, because any physical process can be represented as a quantum channel that transforms an initial state into a final state. Inspired by the method of performing non-unitary operators by the linear combination of unitary operations, we proposed a quantum algorithm for the simulation of the universal single-qubit channel, described by a convex combination of "quasi-extreme" channels corresponding to four Kraus operators, and is scalable to arbitrary higher dimension. We demonstrated the whole algorithm experimentally using the universal IBM cloud-based quantum computer and studied the properties of different qubit quantum channels. We illustrated the quantum capacity of the general qubit quantum channels, which quantifies the amount of quantum information that can be protected. The behavior of quantum capacity in different channels revealed which types of noise processes can support information transmission, and which types are too destructive to protect information. There was a general agreement between the theoretical predictions and the experiments, which strongly supports our method. By realizing the arbitrary qubit channel, this work provides a universally- accepted way to explore various properties of quantum channels and novel prospect for quantum communication.

  15. Quantum Walk in Terms of Quantum Bernoulli Noise and Quantum Central Limit Theorem for Quantum Bernoulli Noise

    Directory of Open Access Journals (Sweden)

    Caishi Wang

    2018-01-01

    Full Text Available As a unitary quantum walk with infinitely many internal degrees of freedom, the quantum walk in terms of quantum Bernoulli noise (recently introduced by Wang and Ye shows a rather classical asymptotic behavior, which is quite different from the case of the usual quantum walks with a finite number of internal degrees of freedom. In this paper, we further examine the structure of the walk. By using the Fourier transform on the state space of the walk, we obtain a formula that links the moments of the walk’s probability distributions directly with annihilation and creation operators on Bernoulli functionals. We also prove some other results on the structure of the walk. Finally, as an application of these results, we establish a quantum central limit theorem for the annihilation and creation operators themselves.

  16. Quantum group and quantum symmetry

    International Nuclear Information System (INIS)

    Chang Zhe.

    1994-05-01

    This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schroedinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion. (author). 133 refs, 20 figs

  17. Quantum arithmetic with the Quantum Fourier Transform

    OpenAIRE

    Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

    2014-01-01

    The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

  18. Quantum logic using correlated one-dimensional quantum walks

    Science.gov (United States)

    Lahini, Yoav; Steinbrecher, Gregory R.; Bookatz, Adam D.; Englund, Dirk

    2018-01-01

    Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.

  19. Special issue on quantum physics with non-Hermitian operators Special issue on quantum physics with non-Hermitian operators

    Science.gov (United States)

    Bender, Carl M.; Fring, Andreas; Guenther, Uwe; Jones, Hugh F.

    2012-01-01

    This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to quantum physics with non-Hermitian operators. The main motivation behind this special issue is to gather together recent results, developments and open problems in this rapidly evolving field of research in a single comprehensive volume. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will be open to all contributions containing new results on non-Hermitian theories which are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. The main novelties in the past years in this area have been many experimental observations, realizations, and applications of PT symmetric Hamiltonians in optics and microwave cavities. We especially invite contributions on the theoretical interpretations of these recent PT-symmetric experiments and on theoretical proposals for new experiments. Editorial policy The Guest Editors for this issue are Carl Bender, Andreas Fring, Uwe Guenther and Hugh Jones. The areas and topics for this issue include, but are not limited to: spectral problems novel properties of complex optical potentials PT-symmetry related threshold lasers and spectral singularities construction of metric operators scattering theory supersymmetric theories Lie algebraic and Krein-space methods random matrix models classical and semi-classical models exceptional points in model systems operator theoretic approaches microwave cavities aspects of integrability and exact solvability field theories with indefinite metric All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 March 2012. This deadline will allow the

  20. Multi-party Semi-quantum Key Agreement with Delegating Quantum Computation

    Science.gov (United States)

    Liu, Wen-Jie; Chen, Zhen-Yu; Ji, Sai; Wang, Hai-Bin; Zhang, Jun

    2017-10-01

    A multi-party semi-quantum key agreement (SQKA) protocol based on delegating quantum computation (DQC) model is proposed by taking Bell states as quantum resources. In the proposed protocol, the participants only need the ability of accessing quantum channel and preparing single photons {|0〉, |1〉, |+〉, |-〉}, while the complicated quantum operations, such as the unitary operations and Bell measurement, will be delegated to the remote quantum center. Compared with previous quantum key agreement protocols, this client-server model is more feasible in the early days of the emergence of quantum computers. In order to prevent the attacks from outside eavesdroppers, inner participants and quantum center, two single photon sequences are randomly inserted into Bell states: the first sequence is used to perform the quantum channel detection, while the second is applied to disorder the positions of message qubits, which guarantees the security of the protocol.

  1. Optical pulse dynamics for quantum-dot logic operations in a photonic-crystal waveguide

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Xun; John, Sajeev [Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 Canada (Canada)

    2011-11-15

    We numerically demonstrate all-optical logic operations with quantum dots (QDs) embedded in a bimodal photonic-crystal waveguide using Maxwell-Bloch equations in a slowly varying envelope approximation (SVEA). The two-level QD excitation level is controlled by one or more femtojoule optical driving pulses passing through the waveguide. Specific logic operations depend on the relative pulse strengths and their detunings from an inhomogeneouslly broadened (about 1% for QD transitions centered at 1.5 {mu}m) QD transition. This excitation controlled two-level medium then determines passage of subsequent probe optical pulses. Envelope equations for electromagnetic waves in the linear dispersion and cutoff waveguide modes are derived to simplify solution of the coupled Maxwell-Bloch equations in the waveguide. These determine the quantum mechanical evolution of the QD excitation and its polarization, driven by classical electromagnetic (EM) pulses near a sharp discontinuity in the EM density of states of the bimodal waveguide. Different configurations of the driving pulses lead to distinctive relations between driving pulse strength and probe pulse passage, representing all-optical logic and, or, and not operations. Simulation results demonstrate that such operations can be done on picosecond time scales and within a waveguide length of about 10 {mu}m in a photonic-band-gap (PBG) optical microchip.

  2. Realization of universal optimal quantum machines by projective operators and stochastic maps

    International Nuclear Information System (INIS)

    Sciarrino, F.; Sias, C.; Ricci, M.; De Martini, F.

    2004-01-01

    Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal antiunitary map. In addition, the contextual realization of the N→M cloning map and of the teleportation of the N→(M-N) universal-NOT (UNOT) gate is analyzed by a very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These include the 1→2 cloning process, the UNOT gate and the quantum tomographic characterization of the optimal partial transpose map of polarization encoded qubits

  3. Quantum probability and quantum decision-making.

    Science.gov (United States)

    Yukalov, V I; Sornette, D

    2016-01-13

    A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary. © 2015 The Author(s).

  4. Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction

    International Nuclear Information System (INIS)

    Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.

    2004-01-01

    It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate C is cumbersome in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method is used to calculate the C operator in quantum field theory. The C operator is a time-independent observable in PT-symmetric quantum field theory

  5. Free-Space Quantum Communication with a Portable Quantum Memory

    Science.gov (United States)

    Namazi, Mehdi; Vallone, Giuseppe; Jordaan, Bertus; Goham, Connor; Shahrokhshahi, Reihaneh; Villoresi, Paolo; Figueroa, Eden

    2017-12-01

    The realization of an elementary quantum network that is intrinsically secure and operates over long distances requires the interconnection of several quantum modules performing different tasks. In this work, we report the realization of a communication network functioning in a quantum regime, consisting of four different quantum modules: (i) a random polarization qubit generator, (ii) a free-space quantum-communication channel, (iii) an ultralow-noise portable quantum memory, and (iv) a qubit decoder, in a functional elementary quantum network possessing all capabilities needed for quantum-information distribution protocols. We create weak coherent pulses at the single-photon level encoding polarization states |H ⟩ , |V ⟩, |D ⟩, and |A ⟩ in a randomized sequence. The random qubits are sent over a free-space link and coupled into a dual-rail room-temperature quantum memory and after storage and retrieval are analyzed in a four-detector polarization analysis akin to the requirements of the BB84 protocol. We also show ultralow noise and fully portable operation, paving the way towards memory-assisted all-environment free-space quantum cryptographic networks.

  6. Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1

    CERN Document Server

    Cremmer, E; Schnittger, J; Cremmer, E; Gervais, J L; Schnittger, J

    1996-01-01

    A simple connection between the universal R matrix of U_q(sl(2)) (for spins \\demi and J) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of U_q(sl(2)) realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended U_q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quant...

  7. Quantum gate decomposition algorithms.

    Energy Technology Data Exchange (ETDEWEB)

    Slepoy, Alexander

    2006-07-01

    Quantum computing algorithms can be conveniently expressed in a format of a quantum logical circuits. Such circuits consist of sequential coupled operations, termed ''quantum gates'', or quantum analogs of bits called qubits. We review a recently proposed method [1] for constructing general ''quantum gates'' operating on an qubits, as composed of a sequence of generic elementary ''gates''.

  8. Improved quantum-inspired evolutionary algorithm with diversity information applied to economic dispatch problem with prohibited operating zones

    International Nuclear Information System (INIS)

    Vianna Neto, Julio Xavier; Andrade Bernert, Diego Luis de; Santos Coelho, Leandro dos

    2011-01-01

    The objective of the economic dispatch problem (EDP) of electric power generation, whose characteristics are complex and highly nonlinear, is to schedule the committed generating unit outputs so as to meet the required load demand at minimum operating cost while satisfying all unit and system equality and inequality constraints. Recently, as an alternative to the conventional mathematical approaches, modern meta-heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in EDPs. Research on merging evolutionary computation and quantum computation has been started since late 1990. Inspired on the quantum computation, this paper presented an improved quantum-inspired evolutionary algorithm (IQEA) based on diversity information of population. A classical quantum-inspired evolutionary algorithm (QEA) and the IQEA were implemented and validated for a benchmark of EDP with 15 thermal generators with prohibited operating zones. From the results for the benchmark problem, it is observed that the proposed IQEA approach provides promising results when compared to various methods available in the literature.

  9. Improved quantum-inspired evolutionary algorithm with diversity information applied to economic dispatch problem with prohibited operating zones

    Energy Technology Data Exchange (ETDEWEB)

    Vianna Neto, Julio Xavier, E-mail: julio.neto@onda.com.b [Pontifical Catholic University of Parana, PUCPR, Undergraduate Program at Mechatronics Engineering, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, Parana (Brazil); Andrade Bernert, Diego Luis de, E-mail: dbernert@gmail.co [Pontifical Catholic University of Parana, PUCPR, Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, Parana (Brazil); Santos Coelho, Leandro dos, E-mail: leandro.coelho@pucpr.b [Pontifical Catholic University of Parana, PUCPR, Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, Parana (Brazil)

    2011-01-15

    The objective of the economic dispatch problem (EDP) of electric power generation, whose characteristics are complex and highly nonlinear, is to schedule the committed generating unit outputs so as to meet the required load demand at minimum operating cost while satisfying all unit and system equality and inequality constraints. Recently, as an alternative to the conventional mathematical approaches, modern meta-heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in EDPs. Research on merging evolutionary computation and quantum computation has been started since late 1990. Inspired on the quantum computation, this paper presented an improved quantum-inspired evolutionary algorithm (IQEA) based on diversity information of population. A classical quantum-inspired evolutionary algorithm (QEA) and the IQEA were implemented and validated for a benchmark of EDP with 15 thermal generators with prohibited operating zones. From the results for the benchmark problem, it is observed that the proposed IQEA approach provides promising results when compared to various methods available in the literature.

  10. Improved quantum-inspired evolutionary algorithm with diversity information applied to economic dispatch problem with prohibited operating zones

    Energy Technology Data Exchange (ETDEWEB)

    Neto, Julio Xavier Vianna [Pontifical Catholic University of Parana, PUCPR, Undergraduate Program at Mechatronics Engineering, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, Parana (Brazil); Bernert, Diego Luis de Andrade; Coelho, Leandro dos Santos [Pontifical Catholic University of Parana, PUCPR, Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, Parana (Brazil)

    2011-01-15

    The objective of the economic dispatch problem (EDP) of electric power generation, whose characteristics are complex and highly nonlinear, is to schedule the committed generating unit outputs so as to meet the required load demand at minimum operating cost while satisfying all unit and system equality and inequality constraints. Recently, as an alternative to the conventional mathematical approaches, modern meta-heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in EDPs. Research on merging evolutionary computation and quantum computation has been started since late 1990. Inspired on the quantum computation, this paper presented an improved quantum-inspired evolutionary algorithm (IQEA) based on diversity information of population. A classical quantum-inspired evolutionary algorithm (QEA) and the IQEA were implemented and validated for a benchmark of EDP with 15 thermal generators with prohibited operating zones. From the results for the benchmark problem, it is observed that the proposed IQEA approach provides promising results when compared to various methods available in the literature. (author)

  11. The operators governing quantum fluctuations of Yang-Mills multi-instantons on S4 and their Seeley coefficients

    International Nuclear Information System (INIS)

    Daniel, M.

    1980-01-01

    We give explicit expressions for the Seeley coefficients of the fluctuation operator and the operator that appears in the Faddeev-Popov determinant, which arise in the calculation of quantum fluctuations around Yang-Mills multi-instantons. (orig.)

  12. Cascade quantum teleportation

    Institute of Scientific and Technical Information of China (English)

    ZHOU Nan-run; GONG Li-hua; LIU Ye

    2006-01-01

    In this letter a cascade quantum teleportation scheme is proposed. The proposed scheme needs less local quantum operations than those of quantum multi-teleportation. A quantum teleportation scheme based on entanglement swapping is presented and compared with the cascade quantum teleportation scheme. Those two schemes can effectively teleport quantum information and extend the distance of quantum communication.

  13. Quantum control limited by quantum decoherence

    International Nuclear Information System (INIS)

    Xue, Fei; Sun, C. P.; Yu, S. X.

    2006-01-01

    We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a decoherence-free quantum control with a finite energy within a finite time. It is also shown that if the operations of quantum control are to be determined by the initial state of the controller, then due to the decoherence which results from the quantum control itself, there exists a low bound for quantum controllability

  14. A full quantum analysis of the Stern–Gerlach experiment using the evolution operator method: analyzing current issues in teaching quantum mechanics

    International Nuclear Information System (INIS)

    Benítez Rodríguez, E; Aguilar, L M Arévalo; Martínez, E Piceno

    2017-01-01

    To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community. (paper)

  15. Quantum secret sharing via local operations and classical communication.

    Science.gov (United States)

    Yang, Ying-Hui; Gao, Fei; Wu, Xia; Qin, Su-Juan; Zuo, Hui-Juan; Wen, Qiao-Yan

    2015-11-20

    We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or "ramp"), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect.

  16. Non-abelian geometrical quantum gate operation in an ultracold strontium gas

    Science.gov (United States)

    Leroux, Frederic

    The work developed in this PhD thesis is about geometric operation on a single qubit. If the external control parameters vary slowly, the quantum system evolves adiabatically in a sub-space composed of two degenerate eigenstates. After a closed loop in the space of the external parameters, the qubit acquires a geometrical rotation, which can be described by a unitary matrix in the Hilbert space of the two-level system. To the geometric rotation corresponds a non-Abelian gauge field. In this work, the qubit and the adiabatic geometrical quantum gates are implemented on a cold gas of atomic Strontium 87, trapped and cooled at the vicinity of the recoil temperature. The internal Hilbert space of the cold atoms has for basis the dressed states issued from the atom-light interaction of three lasers within a tripod configuration.

  17. Entangling quantum-logic gate operated with an ultrabright semiconductor single-photon source.

    Science.gov (United States)

    Gazzano, O; Almeida, M P; Nowak, A K; Portalupi, S L; Lemaître, A; Sagnes, I; White, A G; Senellart, P

    2013-06-21

    We demonstrate the unambiguous entangling operation of a photonic quantum-logic gate driven by an ultrabright solid-state single-photon source. Indistinguishable single photons emitted by a single semiconductor quantum dot in a micropillar optical cavity are used as target and control qubits. For a source brightness of 0.56 photons per pulse, the measured truth table has an overlap with the ideal case of 68.4±0.5%, increasing to 73.0±1.6% for a source brightness of 0.17 photons per pulse. The gate is entangling: At a source brightness of 0.48, the Bell-state fidelity is above the entangling threshold of 50% and reaches 71.0±3.6% for a source brightness of 0.15.

  18. On the definition of the time evolution operator for time-independent Hamiltonians in non-relativistic quantum mechanics

    Science.gov (United States)

    Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.

    2017-09-01

    The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

  19. Quantum decision theory as quantum theory of measurement

    International Nuclear Information System (INIS)

    Yukalov, V.I.; Sornette, D.

    2008-01-01

    We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems

  20. Effects of two-photon absorption on all optical logic operation based on quantum-dot semiconductor optical amplifiers

    Science.gov (United States)

    Zhang, Xiang; Dutta, Niloy K.

    2018-01-01

    We investigate all-optical logic operation in quantum-dot semiconductor optical amplifier (QD-SOA) based Mach-Zehnder interferometer considering the effects of two-photon absorption (TPA). TPA occurs during the propagation of sub-picosecond pulses in QD-SOA, which leads to a change in carrier recovery dynamics in quantum-dots. We utilize a rate equation model to take into account carrier refill through TPA and nonlinear dynamics including carrier heating and spectral hole burning in the QD-SOA. The simulation results show the TPA-induced pumping in the QD-SOA can reduce the pattern effect and increase the output quality of the all-optical logic operation. With TPA, this scheme is suitable for high-speed Boolean logic operation at 320 Gb/s.

  1. Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

    Science.gov (United States)

    Ermilov, A. S.; Zobov, V. E.

    2007-12-01

    To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.

  2. Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators

    Science.gov (United States)

    Siudzińska, Katarzyna; Chruściński, Dariusz

    2018-03-01

    In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.

  3. Blind Quantum Signature with Blind Quantum Computation

    Science.gov (United States)

    Li, Wei; Shi, Ronghua; Guo, Ying

    2017-04-01

    Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

  4. Explicit implementation of quantum circuits on a quantum-cellular-automata-like architecture

    International Nuclear Information System (INIS)

    Kawano, Y.; Yamashita, S.; Kitagawa, M.

    2005-01-01

    We present an efficient strategy to translate a normal quantum algorithm into a sequence of operations on the quantum-cellular-automata-like architecture (QCALA) originally proposed by Lloyd. The QCALA assumes arrays of weakly coupled quantum systems where an interaction exists only between neighboring qubits and can only perform the same quantum operation onto all the qubits. The sequence obtained by the strategy proposed by Lloyd needs at most 12n operations, where n is the number of qubits for the original circuit. The sequence obtained by our strategy needs at most 6n operations. We also clarified the relations between the upper bound of the number of translated operations and the period of the QCALA and between the upper bound of the number of qubits and the period of the QCALA

  5. Overcoming misconceptions in quantum mechanics with the time evolution operator

    International Nuclear Information System (INIS)

    Garcia Quijas, P C; Arevalo Aguilar, L M

    2007-01-01

    Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary states. In this paper, we argue that a possible way to remove these is to solve the Schroedinger equation using the evolution operator method (EOM), and stress the fact that to find stationary states is only the first step in solving that equation. The EOM consists in solving the Schroedinger equation by direct integration, i.e. Ψ(x, t) = U(t)Ψ(x, 0), where U(t)=e -itH-hat/h is the time evolution operator, and Ψ(x, 0) is the initial state. We apply the evolution operator method in the case of the harmonic oscillator

  6. Quantum Mechanics on the h-deformed Quantum Plane

    OpenAIRE

    Cho, Sunggoo

    1998-01-01

    We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended $h$-deformed quantum plane and solve the Schr\\"odinger equations explicitly for some physical systems on the quantum plane. In the commutative limit the behaviour of a quantum particle on the quantum plane becomes that of the quantum particle on the Poincar\\'e half-plane, a surface of constant negative Gaussian curvature. We show the bound state energy spectra for particles under specific poten...

  7. Quantum measurement

    CERN Document Server

    Busch, Paul; Pellonpää, Juha-Pekka; Ylinen, Kari

    2016-01-01

    This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4....

  8. Quantum radar

    CERN Document Server

    Lanzagorta, Marco

    2011-01-01

    This book offers a concise review of quantum radar theory. Our approach is pedagogical, making emphasis on the physics behind the operation of a hypothetical quantum radar. We concentrate our discussion on the two major models proposed to date: interferometric quantum radar and quantum illumination. In addition, this book offers some new results, including an analytical study of quantum interferometry in the X-band radar region with a variety of atmospheric conditions, a derivation of a quantum radar equation, and a discussion of quantum radar jamming.This book assumes the reader is familiar w

  9. Manin's quantum spaces and standard quantum mechanics

    International Nuclear Information System (INIS)

    Floratos, E.G.

    1990-01-01

    Manin's non-commutative coordinate algebra of quantum groups is shown to be identical, for unitary coordinates, with the conventional operator algebras of quantum mechanics. The deformation parameter q is a pure phase for unitary coordinates. When q is a root of unity. Manin's algebra becomes the matrix algebra of quantum mechanics for a discretized and finite phase space. Implications for quantum groups and the associated non-commutative differential calculus of Wess and Zumino are discussed. (orig.)

  10. COmmunications and Networking with QUantum Operationally-Secure Technology for Maritime Deployment (CONQUEST)

    Science.gov (United States)

    2017-03-06

    15 minutes 48 Efficient post -processing for CV QKD Saikat Guha BBN Review Meeting Feb 17, 2017 Communications and Networking with Quantum Operationally...Raytheon BBN Technologies; Dr. Saikat Guha Contractor Address: 10 Moulton Street, Cambridge, MA 02138 Title of the Project: COmmunications and...Equipment Purchased No equipment has been purchased or constructed at this time. Section D. Key Personnel There have been no changes in

  11. Quantum canonical ensemble: A projection operator approach

    Science.gov (United States)

    Magnus, Wim; Lemmens, Lucien; Brosens, Fons

    2017-09-01

    Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.

  12. Quantum metrology

    International Nuclear Information System (INIS)

    Xiang Guo-Yong; Guo Guang-Can

    2013-01-01

    The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts: measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters (e.g., squeezed state and quantum entanglement) yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are. (topical review - quantum information)

  13. Quantum Variational Calculus

    OpenAIRE

    Malinowska , Agnieszka B.; Torres , Delfim

    2014-01-01

    International audience; Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of it...

  14. Nonadiabatic corrections to a quantum dot quantum computer

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 83; Issue 1. Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit. M Ávila ... The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the ...

  15. A charged particle interacting with a stationary magnetic monopole: quantum mechanics based on the kinetic momentum operators

    International Nuclear Information System (INIS)

    Raković, Milun J

    2011-01-01

    The standard quantum mechanical description of the motion of a charged particle in the field of a stationary magnetic monopole is notorious for the presence of unnatural singularities in the Hamiltonian operator originating in the vector potential A(r) used to describe the magnetic field of the monopole. In this paper, an elementary quantum mechanical formulation of the problem which involves only the physically observable field B(r) is presented. This is achieved by treating as a fundamental observable of the charged particle its kinetic momentum instead of the linear momentum p. An irreducible representation of the fundamental commutation relations involving the operators r-hat. It is shown that the existence of an irreducible representation requires that Dirac’s charge quantization condition is satisfied. Also, it is demonstrated that, from the quantum mechanical perspective, the singularities (appearing when the vector potential is introduced) are in fact properties of coordinate representations of the fundamental commutation relations. (paper)

  16. Generalized Hofmann quantum process fidelity bounds for quantum filters

    Science.gov (United States)

    Sedlák, Michal; Fiurášek, Jaromír

    2016-04-01

    We propose and investigate bounds on the quantum process fidelity of quantum filters, i.e., probabilistic quantum operations represented by a single Kraus operator K . These bounds generalize the Hofmann bounds on the quantum process fidelity of unitary operations [H. F. Hofmann, Phys. Rev. Lett. 94, 160504 (2005), 10.1103/PhysRevLett.94.160504] and are based on probing the quantum filter with pure states forming two mutually unbiased bases. Determination of these bounds therefore requires far fewer measurements than full quantum process tomography. We find that it is particularly suitable to construct one of the probe bases from the right eigenstates of K , because in this case the bounds are tight in the sense that if the actual filter coincides with the ideal one, then both the lower and the upper bounds are equal to 1. We theoretically investigate the application of these bounds to a two-qubit optical quantum filter formed by the interference of two photons on a partially polarizing beam splitter. For an experimentally convenient choice of factorized input states and measurements we study the tightness of the bounds. We show that more stringent bounds can be obtained by more sophisticated processing of the data using convex optimization and we compare our methods for different choices of the input probe states.

  17. Raising and lowering operators for quantum billiards

    Indian Academy of Sciences (India)

    AYUSH KUMAR MANDWAL

    2017-08-16

    Aug 16, 2017 ... Abstract. For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as m, n, the index which represents a class is c = m mod kn for a natural number, k. We show here that the entire tower of states can be ...

  18. Raising and lowering operators for quantum billiards

    Indian Academy of Sciences (India)

    For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as m , n , the index which represents a class is c = m mod k n for a natural number, k . We show here that the entire tower of states can be generated from an initially ...

  19. Operational tools for moment characterization, entanglement verification and quantum key distribution

    International Nuclear Information System (INIS)

    Moroder, Tobias

    2009-01-01

    In this thesis we address several different topics within the field of quantum information theory. These results can be classified to either enhance the applicability of certain conceptual ideas to be more suited for an actual experimental situation or to ease the analysis for further investigation of central problems. In detail, the present thesis contains the following achievements: We start our discussion with the question under which conditions a given set of expectation values is compatible with the first and second moments of the spin operators of a generic spin j state. We link this characterization of physical moments to the Bosesymmetric extension problem for a particular two qubit state that is completely determined by the given moments. Via this reformulation we can provide operational sub- and superset approximations in order to identify moments which are assured to be physical and others which are clearly incompatible with quantum mechanics. We show that this operational approximate solution becomes more accurate for increasing total spin numbers j and converges to the exact solution in the limiting case. Another part deals with the theoretical concept of entanglement witnesses. In particular, we concentrate how to improve the detection strength of a linear entanglement witness by nonlinear terms. We analyze two distinguished cases: Either we optimize the iteration method for a given target state or we try to improve the entanglement witness with respect to all entangled states equally. In the remaining parts we discuss different options in order to make already existing ideas more applicable for actual experiments, since most of the famous applications in quantum information theory have only been introduced on a very idealized level and hence are not directly valid for the real experiment. We investigate the theoretical concept of a squash model, that represents an elegant ''evaluation trick'' to directly apply for instance the security analysis of an

  20. Operational tools for moment characterization, entanglement verification and quantum key distribution

    Energy Technology Data Exchange (ETDEWEB)

    Moroder, Tobias

    2009-07-31

    In this thesis we address several different topics within the field of quantum information theory. These results can be classified to either enhance the applicability of certain conceptual ideas to be more suited for an actual experimental situation or to ease the analysis for further investigation of central problems. In detail, the present thesis contains the following achievements: We start our discussion with the question under which conditions a given set of expectation values is compatible with the first and second moments of the spin operators of a generic spin j state. We link this characterization of physical moments to the Bosesymmetric extension problem for a particular two qubit state that is completely determined by the given moments. Via this reformulation we can provide operational sub- and superset approximations in order to identify moments which are assured to be physical and others which are clearly incompatible with quantum mechanics. We show that this operational approximate solution becomes more accurate for increasing total spin numbers j and converges to the exact solution in the limiting case. Another part deals with the theoretical concept of entanglement witnesses. In particular, we concentrate how to improve the detection strength of a linear entanglement witness by nonlinear terms. We analyze two distinguished cases: Either we optimize the iteration method for a given target state or we try to improve the entanglement witness with respect to all entangled states equally. In the remaining parts we discuss different options in order to make already existing ideas more applicable for actual experiments, since most of the famous applications in quantum information theory have only been introduced on a very idealized level and hence are not directly valid for the real experiment. We investigate the theoretical concept of a squash model, that represents an elegant ''evaluation trick'' to directly apply for instance the

  1. Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Delfino, G. [International School of Advanced Studies (SISSA), Trieste (Italy)]|[INFN sezione di Trieste (Italy); Niccoli, G. [Univ. de Cergy-Pontoise (France). LPTM

    2007-12-15

    For the simplest quantum field theory originating from a non-trivial fixed point of the renormalization group, the Lee-Yang model, we show that the operator space determined by the particle dynamics in the massive phase and that prescribed by conformal symmetry at criticality coincide. (orig.)

  2. Quantum thermodynamics

    International Nuclear Information System (INIS)

    Beretta, G.P.; Gyftopoulos, E.P.; Park, J.L.

    1985-01-01

    A novel nonlinear equation of motion is proposed for a general quantum system consisting of more than one distinguishable elementary constituent of matter. In the domain of idempotent quantum-mechanical state operators, it is satisfied by all unitary evolutions generated by the Schroedinger equation. But in the broader domain of nonidempotent state operators not contemplated by conventional quantum mechanics, it generates a generally nonunitary evolution, it keeps the energy invariant and causes the entropy to increase with time until the system reaches a state of equilibrium or a limit cycle

  3. Extended quantum mechanics

    International Nuclear Information System (INIS)

    Pavel Bona

    2000-01-01

    The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics which is related here to some other (more general, but also to more special and 'approximative') theories. Quantum mechanics is here primarily reformulated in an equivalent form of a Poisson system on the phase space consisting of density matrices, where the 'observables', as well as 'symmetry generators' are represented by a specific type of real valued (densely defined) functions, namely the usual quantum expectations of corresponding selfjoint operators. It is shown in this paper that inclusion of additional ('nonlinear') symmetry generators (i. e. 'Hamiltonians') into this reformulation of (linear) quantum mechanics leads to a considerable extension of the theory: two kinds of quantum 'mixed states' should be distinguished, and operator - valued functions of density matrices should be used in the role of 'nonlinear observables'. A general framework for physical theories is obtained in this way: By different choices of the sets of 'nonlinear observables' we obtain, as special cases, e.g. classical mechanics on homogeneous spaces of kinematical symmetry groups, standard (linear) quantum mechanics, or nonlinear extensions of quantum mechanics; also various 'quasiclassical approximations' to quantum mechanics are all sub theories of the presented extension of quantum mechanics - a version of the extended quantum mechanics. A general interpretation scheme of extended quantum mechanics extending the usual statistical interpretation of quantum mechanics is also proposed. Eventually, extended quantum mechanics is shown to be (included into) a C * -algebraic (hence linear) quantum theory. Mathematical formulation of these theories is presented. The presentation includes an analysis of problems connected with differentiation on infinite-dimensional manifolds, as well as a solution of some problems connected with the work with only densely defined unbounded

  4. Quantum Computation-Based Image Representation, Processing Operations and Their Applications

    Directory of Open Access Journals (Sweden)

    Fei Yan

    2014-10-01

    Full Text Available A flexible representation of quantum images (FRQI was proposed to facilitate the extension of classical (non-quantum-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI, quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.

  5. Layered Architectures for Quantum Computers and Quantum Repeaters

    Science.gov (United States)

    Jones, Nathan C.

    This chapter examines how to organize quantum computers and repeaters using a systematic framework known as layered architecture, where machine control is organized in layers associated with specialized tasks. The framework is flexible and could be used for analysis and comparison of quantum information systems. To demonstrate the design principles in practice, we develop architectures for quantum computers and quantum repeaters based on optically controlled quantum dots, showing how a myriad of technologies must operate synchronously to achieve fault-tolerance. Optical control makes information processing in this system very fast, scalable to large problem sizes, and extendable to quantum communication.

  6. The thermodynamic cost of quantum operations

    International Nuclear Information System (INIS)

    Bedingham, D J; Maroney, O J E

    2016-01-01

    The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower bound is set by the Landauer limit, at which computation becomes thermodynamically reversible. For classical computation there is no physical principle which prevents this limit being reached, and approaches to it are already being experimentally tested. In this paper we show that for quantum computation with a set of signal states satisfying given conditions, there is an unavoidable excess heat generation that renders it inherently thermodynamically irreversible. The Landauer limit cannot, in general, be reached by quantum computers. We show the existence of a lower bound to the heat generated by quantum computing that exceeds that given by the Landauer limit, give the special conditions where this excess cost may be avoided, and provide a protocol for achieving the limiting heat cost when these conditions are met. We also show how classical computing falls within the special conditions. (paper)

  7. Quantum demultiplexer of quantum parameter-estimation information in quantum networks

    Science.gov (United States)

    Xie, Yanqing; Huang, Yumeng; Wu, Yinzhong; Hao, Xiang

    2018-05-01

    The quantum demultiplexer is constructed by a series of unitary operators and multipartite entangled states. It is used to realize information broadcasting from an input node to multiple output nodes in quantum networks. The scheme of quantum network communication with respect to phase estimation is put forward through the demultiplexer subjected to amplitude damping noises. The generalized partial measurements can be applied to protect the transferring efficiency from environmental noises in the protocol. It is found out that there are some optimal coherent states which can be prepared to enhance the transmission of phase estimation. The dynamics of state fidelity and quantum Fisher information are investigated to evaluate the feasibility of the network communication. While the state fidelity deteriorates rapidly, the quantum Fisher information can be enhanced to a maximum value and then decreases slowly. The memory effect of the environment induces the oscillations of fidelity and quantum Fisher information. The adjustment of the strength of partial measurements is helpful to increase quantum Fisher information.

  8. Molecular machines operating on the nanoscale: from classical to quantum

    Directory of Open Access Journals (Sweden)

    Igor Goychuk

    2016-03-01

    Full Text Available The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

  9. Daylight operation of a free space, entanglement-based quantum key distribution system

    Energy Technology Data Exchange (ETDEWEB)

    Peloso, Matthew P; Gerhardt, Ilja; Ho, Caleb; Lamas-Linares, AntIa; Kurtsiefer, Christian [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)], E-mail: christian.kurtsiefer@gmail.com

    2009-04-15

    Many quantum key distribution (QKD) implementations using a free space transmission path are restricted to operation at night time in order to distinguish the signal photons used for a secure key establishment from the background light. Here, we present a lean entanglement-based QKD system overcoming that limitation. By implementing spectral, spatial and temporal filtering techniques, we establish a secure key continuously over several days under varying light and weather conditions.

  10. Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels

    International Nuclear Information System (INIS)

    Deutsch, D.; Ekert, A.; Jozsa, R.; Macchiavello, C.; Popescu, S.; Sanpera, A.

    1996-01-01

    Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyze and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an open-quote open-quote entanglement purification close-quote close-quote procedure which, because it requires only a few quantum controlled-not and single-qubit operations, could be implemented using technology that is currently being developed. copyright 1996 The American Physical Society

  11. Distinct Lasing Operation From Chirped InAs/InP Quantum-Dash Laser

    KAUST Repository

    Khan, Mohammed Zahed Mustafa

    2013-08-01

    We study the enhanced inhomogeneity across the InAs quantum-dash (Qdash) layers by incorporating a chirped AlGaInAs barrier thickness in the InAs/InP laser structure. The lasing operation is investigated via Fabry-Pérot ridge-waveguide laser characterization, which shows a peculiar behavior under quasi-continuous-wave (QCW) operation. Continuous energy transfer between different dash ensembles initiated quenching of lasing action among certain dash groups, causing a reduced intensity gap in the lasing spectra. We discuss these characteristics in terms of the quasi-zero-dimensional density of states (DOS) of dashes and the active region inhomogeneity. © 2009-2012 IEEE.

  12. Generalized Bell states map physical systems’ quantum evolution into a grammar for quantum information processing

    Science.gov (United States)

    Delgado, Francisco

    2017-12-01

    Quantum information processing should be generated through control of quantum evolution for physical systems being used as resources, such as superconducting circuits, spinspin couplings in ions and artificial anyons in electronic gases. They have a quantum dynamics which should be translated into more natural languages for quantum information processing. On this terrain, this language should let to establish manipulation operations on the associated quantum information states as classical information processing does. This work shows how a kind of processing operations can be settled and implemented for quantum states design and quantum processing for systems fulfilling a SU(2) reduction in their dynamics.

  13. Scalable optical quantum computer

    International Nuclear Information System (INIS)

    Manykin, E A; Mel'nichenko, E V

    2014-01-01

    A way of designing a scalable optical quantum computer based on the photon echo effect is proposed. Individual rare earth ions Pr 3+ , regularly located in the lattice of the orthosilicate (Y 2 SiO 5 ) crystal, are suggested to be used as optical qubits. Operations with qubits are performed using coherent and incoherent laser pulses. The operation protocol includes both the method of measurement-based quantum computations and the technique of optical computations. Modern hybrid photon echo protocols, which provide a sufficient quantum efficiency when reading recorded states, are considered as most promising for quantum computations and communications. (quantum computer)

  14. Chiral quantum optics.

    Science.gov (United States)

    Lodahl, Peter; Mahmoodian, Sahand; Stobbe, Søren; Rauschenbeutel, Arno; Schneeweiss, Philipp; Volz, Jürgen; Pichler, Hannes; Zoller, Peter

    2017-01-25

    Advanced photonic nanostructures are currently revolutionizing the optics and photonics that underpin applications ranging from light technology to quantum-information processing. The strong light confinement in these structures can lock the local polarization of the light to its propagation direction, leading to propagation-direction-dependent emission, scattering and absorption of photons by quantum emitters. The possibility of such a propagation-direction-dependent, or chiral, light-matter interaction is not accounted for in standard quantum optics and its recent discovery brought about the research field of chiral quantum optics. The latter offers fundamentally new functionalities and applications: it enables the assembly of non-reciprocal single-photon devices that can be operated in a quantum superposition of two or more of their operational states and the realization of deterministic spin-photon interfaces. Moreover, engineered directional photonic reservoirs could lead to the development of complex quantum networks that, for example, could simulate novel classes of quantum many-body systems.

  15. Negative inductance SQUID qubit operating in a quantum regime

    Science.gov (United States)

    Liu, W. Y.; Su, F. F.; Xu, H. K.; Li, Z. Y.; Tian, Ye; Zhu, X. B.; Lu, Li; Han, Siyuan; Zhao, S. P.

    2018-04-01

    Two-junction SQUIDs with negative mutual inductance between their two arms, called nSQUIDs, have been proposed for significantly improving quantum information transfer but their quantum nature has not been experimentally demonstrated. We have designed, fabricated, and characterized superconducting nSQUID qubits. Our results provide clear evidence of the quantum coherence of the device, whose properties are well described by theoretical calculations using parameters determined from spectroscopic measurement. In addition to their future application for fast quantum information transfer, the nSQUID qubits exhibit rich characteristics in their tunable two-dimensional (2D) potentials, energy levels, wave function symmetries, and dipole matrix elements, which are essential to the study of a wide variety of macroscopic quantum phenomena such as tunneling in 2D potential landscapes.

  16. A quantum Fredkin gate.

    Science.gov (United States)

    Patel, Raj B; Ho, Joseph; Ferreyrol, Franck; Ralph, Timothy C; Pryde, Geoff J

    2016-03-01

    Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently.

  17. A quantum Fredkin gate

    Science.gov (United States)

    Patel, Raj B.; Ho, Joseph; Ferreyrol, Franck; Ralph, Timothy C.; Pryde, Geoff J.

    2016-01-01

    Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently. PMID:27051868

  18. Quantum Dialogue by Using Non-Symmetric Quantum Channel

    International Nuclear Information System (INIS)

    Zhan Youbang; Zhang Lingling; Zhang Qunyong; Wang Yuwu

    2010-01-01

    A protocol for quantum dialogue is proposed to exchange directly the communicator's secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence coding, local collective unitary operations, and entanglement swapping. In this protocol, during the process of transmission of particles, the transmitted particles do not carry any secret messages and are transmitted only one time. The protocol has higher source capacity than protocols using symmetric two-dimensional states. The security is ensured by the unitary operations randomly performed on all checking groups before the particle sequence is transmitted and the application of entanglement swapping. (general)

  19. Quantifying quantum coherence with quantum Fisher information.

    Science.gov (United States)

    Feng, X N; Wei, L F

    2017-11-14

    Quantum coherence is one of the old but always important concepts in quantum mechanics, and now it has been regarded as a necessary resource for quantum information processing and quantum metrology. However, the question of how to quantify the quantum coherence has just been paid the attention recently (see, e.g., Baumgratz et al. PRL, 113. 140401 (2014)). In this paper we verify that the well-known quantum Fisher information (QFI) can be utilized to quantify the quantum coherence, as it satisfies the monotonicity under the typical incoherent operations and the convexity under the mixing of the quantum states. Differing from most of the pure axiomatic methods, quantifying quantum coherence by QFI could be experimentally testable, as the bound of the QFI is practically measurable. The validity of our proposal is specifically demonstrated with the typical phase-damping and depolarizing evolution processes of a generic single-qubit state, and also by comparing it with the other quantifying methods proposed previously.

  20. Turbocharging Quantum Tomography

    Energy Technology Data Exchange (ETDEWEB)

    Blume-Kohout, Robin J. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Gamble, John King [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Nielsen, Erik [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Maunz, Peter Lukas Wilhelm [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Scholten, Travis L. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rudinger, Kenneth Michael [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

    2015-01-01

    Quantum tomography is used to characterize quantum operations implemented in quantum information processing (QIP) hardware. Traditionally, state tomography has been used to characterize the quantum state prepared in an initialization procedure, while quantum process tomography is used to characterize dynamical operations on a QIP system. As such, tomography is critical to the development of QIP hardware (since it is necessary both for debugging and validating as-built devices, and its results are used to influence the next generation of devices). But tomography suffers from several critical drawbacks. In this report, we present new research that resolves several of these flaws. We describe a new form of tomography called gate set tomography (GST), which unifies state and process tomography, avoids prior methods critical reliance on precalibrated operations that are not generally available, and can achieve unprecedented accuracies. We report on theory and experimental development of adaptive tomography protocols that achieve far higher fidelity in state reconstruction than non-adaptive methods. Finally, we present a new theoretical and experimental analysis of process tomography on multispin systems, and demonstrate how to more effectively detect and characterize quantum noise using carefully tailored ensembles of input states.

  1. Quantum stochastics

    CERN Document Server

    Chang, Mou-Hsiung

    2015-01-01

    The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...

  2. Nonlinear operators and nonlinear transformations studied via the differential form of the completeness relation in quantum mechanics

    International Nuclear Information System (INIS)

    Fan Hongyi; Yu Shenxi

    1994-01-01

    We show that the differential form of the fundamental completeness relation in quantum mechanics and the technique of differentiation within an ordered product (DWOP) of operators provide a new approach for calculating normal product expansions of some nonlinear operators and study some nonlinear transformations. Their usefulness in perturbative calculations is pointed out. (orig.)

  3. Operator-normalized quantum arrival times in the presence of interactions

    International Nuclear Information System (INIS)

    Hegerfeldt, G.C.; Seidel, D.; Muga, J.G.; Navarro, B.

    2004-01-01

    We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring the first photon emitted from a two-level atom illuminated by a laser. By operator normalizing the resulting time-of-arrival distribution, a distribution is obtained which for freely moving particles not only recovers the axiomatically derived distribution of Kijowski for states with purely positive momenta but is also applicable to general momentum components. For particles interacting with a square barrier the mean arrival time and corresponding 'tunneling time' obtained at the transmission side of the barrier become independent of the barrier width (Hartman effect) for arbitrarily wide barriers, i.e., without the transition to the ultraopaque, classical-like regime dominated by wave packet components above the barrier

  4. Dissipative quantum error correction and application to quantum sensing with trapped ions.

    Science.gov (United States)

    Reiter, F; Sørensen, A S; Zoller, P; Muschik, C A

    2017-11-28

    Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error-correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.

  5. Operator ordering in quantum optics theory and the development of Dirac's symbolic method

    International Nuclear Information System (INIS)

    Fan Hongyi

    2003-01-01

    We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented. (review article)

  6. Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

    Directory of Open Access Journals (Sweden)

    Stefan Hollands

    2009-09-01

    Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.

  7. Non-unitary probabilistic quantum computing circuit and method

    Science.gov (United States)

    Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)

    2009-01-01

    A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.

  8. Scalable optical quantum computer

    Energy Technology Data Exchange (ETDEWEB)

    Manykin, E A; Mel' nichenko, E V [Institute for Superconductivity and Solid-State Physics, Russian Research Centre ' Kurchatov Institute' , Moscow (Russian Federation)

    2014-12-31

    A way of designing a scalable optical quantum computer based on the photon echo effect is proposed. Individual rare earth ions Pr{sup 3+}, regularly located in the lattice of the orthosilicate (Y{sub 2}SiO{sub 5}) crystal, are suggested to be used as optical qubits. Operations with qubits are performed using coherent and incoherent laser pulses. The operation protocol includes both the method of measurement-based quantum computations and the technique of optical computations. Modern hybrid photon echo protocols, which provide a sufficient quantum efficiency when reading recorded states, are considered as most promising for quantum computations and communications. (quantum computer)

  9. Gate errors in solid-state quantum-computer architectures

    International Nuclear Information System (INIS)

    Hu Xuedong; Das Sarma, S.

    2002-01-01

    We theoretically consider possible errors in solid-state quantum computation due to the interplay of the complex solid-state environment and gate imperfections. In particular, we study two examples of gate operations in the opposite ends of the gate speed spectrum, an adiabatic gate operation in electron-spin-based quantum dot quantum computation and a sudden gate operation in Cooper-pair-box superconducting quantum computation. We evaluate quantitatively the nonadiabatic operation of a two-qubit gate in a two-electron double quantum dot. We also analyze the nonsudden pulse gate in a Cooper-pair-box-based quantum-computer model. In both cases our numerical results show strong influences of the higher excited states of the system on the gate operation, clearly demonstrating the importance of a detailed understanding of the relevant Hilbert-space structure on the quantum-computer operations

  10. Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

    International Nuclear Information System (INIS)

    Dong Ping; Yang Ming; Cao Zhuoliang

    2008-01-01

    In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

  11. Entanglement Potential Versus Negativity of Wigner Function for SUP-Operated Quantum States

    Science.gov (United States)

    Chatterjee, Arpita

    2018-02-01

    We construct a distinct category of nonclassical quantum states by applying a superposition of products (SUP) of field annihilation (\\hat {a}) and creation (\\hat {a}^{\\dagger }) operators of the type (s\\hat {a}\\hat {a}^{\\dagger }+t\\hat {a}^{\\dagger }\\hat {a}), with s2+t2=1, upon thermal and even coherent states. We allow these SUP operated states to undergo a decoherence process and then describe the nonclassical features of the resulted field by using the entanglement potential (EP) and the negativity of the Wigner distribution function. Our analysis reveals that both the measures are reduced in the linear loss process. The partial negativity of the Wigner function disappears when losses exceed 50% but EP exists always.

  12. Realistic neurons can compute the operations needed by quantum probability theory and other vector symbolic architectures.

    Science.gov (United States)

    Stewart, Terrence C; Eliasmith, Chris

    2013-06-01

    Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).

  13. Quantum information processing beyond ten ion-qubits

    International Nuclear Information System (INIS)

    Monz, T.

    2011-01-01

    Successful processing of quantum information is, to a large degree, based on two aspects: a) the implementation of high-fidelity quantum gates, as well as b) avoiding or suppressing decoherence processes that destroy quantum information. The presented work shows our progress in the field of experimental quantum information processing over the last years: the implementation and characterisation of several quantum operations, amongst others the first realisation of the quantum Toffoli gate in an ion-trap based quantum computer. The creation of entangled states with up to 14 qubits serves as basis for investigations of decoherence processes. Based on the realised quantum operations as well as the knowledge about dominant noise processes in the employed apparatus, entanglement swapping as well as quantum operations within a decoherence-free subspace are demonstrated. (author) [de

  14. Quantum cryptography and quantification of quantum correlations

    International Nuclear Information System (INIS)

    Koashi, M

    2008-01-01

    Study of the security of quantum key distribution protocols has provided us a deeper understanding about the trade-off between the amount of information extracted from a quantum system and the disturbance left in the system as a result of the extraction process. Here we discuss how such a new development helps us to understand the quantum correlations in a quantitative way. A detailed analysis of the information-disturbance trade-off for the zero-disturbance cases leads to a simple structure theorem, and the theorem can be used to derive an exact formula for the compressibility of quantum signals, which is a measure of quantum correlations in terms of the cost to preserve them. The analysis including the nonzero disturbance cases has a very close connection to the theory of entanglement. While the distillable key is regarded as a measure of entanglement, it does not coincide with either of the two operational measures of entanglement, the distillable entanglement and the entanglement cost. We discuss the physical meaning of the difference between these three measures of entanglement by providing each of them with an alternative operational definition

  15. Quantum walks with entangled coins

    International Nuclear Information System (INIS)

    Venegas-Andraca, S E; Ball, J L; Burnett, K; Bose, S

    2005-01-01

    We present a mathematical formalism for the description of un- restricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, with two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on two and three qubit coins leads to different position probability distributions in one- and two-dimensional graphs

  16. Quantum computer with mixed states and four-valued logic

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2002-01-01

    In this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4 n -dimensional operator Hilbert space (Liouville space). It allows us to use a quantum computer model with four-valued logic. The gates of this model are general superoperators which act on n-ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n-qubit open system are considered as four-valued logic gates acting on n-ququats. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates. (author)

  17. Singularity resolution in quantum gravity

    International Nuclear Information System (INIS)

    Husain, Viqar; Winkler, Oliver

    2004-01-01

    We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity

  18. Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups

    CERN Document Server

    2017-01-01

    Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...

  19. Quantum Metropolis sampling.

    Science.gov (United States)

    Temme, K; Osborne, T J; Vollbrecht, K G; Poulin, D; Verstraete, F

    2011-03-03

    The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.

  20. Quantum Gate Operations in Decoherence-Free Subspace with Superconducting Charge Qubits inside a Cavity

    International Nuclear Information System (INIS)

    Yi-Min, Wang; Yan-Li, Zhou; Lin-Mei, Liang; Cheng-Zu, Li

    2009-01-01

    We propose a feasible scheme to achieve universal quantum gate operations in decoherence-free subspace with superconducting charge qubits placed in a microwave cavity. Single-logic-qubit gates can be realized with cavity assisted interaction, which possesses the advantages of unconventional geometric gate operation. The two-logic-qubit controlled-phase gate between subsystems can be constructed with the help of a variable electrostatic transformer. The collective decoherence can be successfully avoided in our well-designed system. Moreover, GHZ state for logical qubits can also be easily produced in this system

  1. Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings

    International Nuclear Information System (INIS)

    Engle, J

    2007-01-01

    In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of Engle (2006 Quantum field theory and its symmetry reduction Class. Quantum Gravity 23 2861-94). We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions

  2. Quantum mechanics with non-negative quantum distribution function

    International Nuclear Information System (INIS)

    Zorin, A.V.; Sevastianov, L.A.

    2010-01-01

    Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

  3. Bipartite separability and nonlocal quantum operations on graphs

    Science.gov (United States)

    Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.

    2016-07-01

    In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

  4. General decoupling procedure for expectation values of four-operator products in electron–phonon quantum kinetics

    International Nuclear Information System (INIS)

    Teeny, Nicolas; Fähnle, Manfred

    2013-01-01

    In the density-matrix formalism of electron–phonon quantum kinetics, the hierarchy of infinitely many coupled equations of motion for the expectation values of products of electron and phonon creation and annihilation operators of arbitrary order is usually terminated on the level of the equations of motion for the expectation values of three-operator products by using decoupling procedures for the four-operator products occurring in these equations. In the literature, decoupling procedures are discussed for special types of electron and phonon states. In the present paper, generalized decoupling procedures are derived for arbitrary electron and phonon states. (paper)

  5. Gossip algorithms in quantum networks

    International Nuclear Information System (INIS)

    Siomau, Michael

    2017-01-01

    Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip algorithms to quantum networks and show that any quantum network can be updated to optimal configuration with local operations and classical communication. This allows to speed-up – in the best case exponentially – the quantum information dissemination. Irrespective of the initial configuration of the quantum network, the update requiters at most polynomial number of local operations and classical communication. - Highlights: • We analyze the performance of gossip algorithms in quantum networks. • Local operations and classical communication (LOCC) can speed the performance up. • The speed-up is exponential in the best case; the number of LOCC is polynomial.

  6. Gossip algorithms in quantum networks

    Energy Technology Data Exchange (ETDEWEB)

    Siomau, Michael, E-mail: siomau@nld.ds.mpg.de [Physics Department, Jazan University, P.O. Box 114, 45142 Jazan (Saudi Arabia); Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany)

    2017-01-23

    Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip algorithms to quantum networks and show that any quantum network can be updated to optimal configuration with local operations and classical communication. This allows to speed-up – in the best case exponentially – the quantum information dissemination. Irrespective of the initial configuration of the quantum network, the update requiters at most polynomial number of local operations and classical communication. - Highlights: • We analyze the performance of gossip algorithms in quantum networks. • Local operations and classical communication (LOCC) can speed the performance up. • The speed-up is exponential in the best case; the number of LOCC is polynomial.

  7. Benchmarking gate-based quantum computers

    Science.gov (United States)

    Michielsen, Kristel; Nocon, Madita; Willsch, Dennis; Jin, Fengping; Lippert, Thomas; De Raedt, Hans

    2017-11-01

    With the advent of public access to small gate-based quantum processors, it becomes necessary to develop a benchmarking methodology such that independent researchers can validate the operation of these processors. We explore the usefulness of a number of simple quantum circuits as benchmarks for gate-based quantum computing devices and show that circuits performing identity operations are very simple, scalable and sensitive to gate errors and are therefore very well suited for this task. We illustrate the procedure by presenting benchmark results for the IBM Quantum Experience, a cloud-based platform for gate-based quantum computing.

  8. Probabilistic structure of quantum theory

    International Nuclear Information System (INIS)

    Burzynski, A.

    1989-01-01

    The fundamental ideas of quantum theory are presented. It is shown that two approaches to quantum theory: Heisenberg's matrix mechanics and Schroedinger's wave mechanics, can be formulated by means of the theory of operators in Hilbert space. Some remarks on Hilbert spaces, diadic and projection operators are done. States, probabilities and observables of quantum systems are discussed and time evolution of quantum states is analysed. Some remarks on two-component systems and symmetries are given. 21 refs. (M.F.W.)

  9. The eigenfunction method and the mass operator in intense-field quantum electrodynamics

    International Nuclear Information System (INIS)

    Ritus, V.I.

    1987-01-01

    A method is given for calculating radiation effects in constant intense-field quantum electrodynamics; this method is based on the use of the eigenfunctions of the mass operator and diagonalization of the latter. A compact expression is found for the eigenvalue of the mass operator of the electron in a random constant field together with the corresponding elastic scattering amplitude. The anomalous electric moment that arises in the field with a pseudoscalar EH not equal to O is found and investigated in detail together with the anomalous magnetic moment in the electrical field that approaches the double Schwinger value with an increase in the field together with the mass shift and the rate of decay of the ground state of the electron in the electrical field

  10. Quantum signaling game

    International Nuclear Information System (INIS)

    Frackiewicz, Piotr

    2014-01-01

    We present a quantum approach to a signaling game; a special kind of extensive game of incomplete information. Our model is based on quantum schemes for games in strategic form where players perform unitary operators on their own qubits of some fixed initial state and the payoff function is given by a measurement on the resulting final state. We show that the quantum game induced by our scheme coincides with a signaling game as a special case and outputs nonclassical results in general. As an example, we consider a quantum extension of the signaling game in which the chance move is a three-parameter unitary operator whereas the players' actions are equivalent to classical ones. In this case, we study the game in terms of Nash equilibria and refine the pure Nash equilibria adapting to the quantum game the notion of a weak perfect Bayesian equilibrium. (paper)

  11. Canonical Quantum Teleportation of Two-Particle Arbitrary State

    Institute of Scientific and Technical Information of China (English)

    HAO Xiang; ZHU Shi-Qun

    2005-01-01

    The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.

  12. Quantum Dot Systems: a versatile platform for quantum simulations

    International Nuclear Information System (INIS)

    Barthelemy, Pierre; Vandersypen, Lieven M.K.

    2013-01-01

    Quantum mechanics often results in extremely complex phenomena, especially when the quantum system under consideration is composed of many interacting particles. The states of these many-body systems live in a space so large that classical numerical calculations cannot compute them. Quantum simulations can be used to overcome this problem: complex quantum problems can be solved by studying experimentally an artificial quantum system operated to simulate the desired hamiltonian. Quantum dot systems have shown to be widely tunable quantum systems, that can be efficiently controlled electrically. This tunability and the versatility of their design makes them very promising quantum simulators. This paper reviews the progress towards digital quantum simulations with individually controlled quantum dots, as well as the analog quantum simulations that have been performed with these systems. The possibility to use large arrays of quantum dots to simulate the low-temperature Hubbard model is also discussed. The main issues along that path are presented and new ideas to overcome them are proposed. (copyright 2013 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  13. Distributed quantum information processing via quantum dot spins

    International Nuclear Information System (INIS)

    Jun, Liu; Qiong, Wang; Le-Man, Kuang; Hao-Sheng, Zeng

    2010-01-01

    We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins. Along with one-qubit local operations, one can in principal perform various types of distributed quantum information processing. The scheme employs a photon with linearly polarisation interacting one after the other with two remote quantum-dot spins in cavities. Due to the optical spin selection rule, the photon obtains a Faraday rotation after the interaction process. By measuring the polarisation of the final output photon, a non-local two-qubit phase gate between the two remote quantum-dot spins is constituted. Our scheme may has very important applications in the distributed quantum information processing

  14. Probabilistic Teleportation of Arbitrary Two-Qubit Quantum State via Non-Symmetric Quantum Channel

    Directory of Open Access Journals (Sweden)

    Kan Wang

    2018-03-01

    Full Text Available Quantum teleportation has significant meaning in quantum information. In particular, entangled states can also be used for perfectly teleporting the quantum state with some probability. This is more practical and efficient in practice. In this paper, we propose schemes to use non-symmetric quantum channel combinations for probabilistic teleportation of an arbitrary two-qubit quantum state from sender to receiver. The non-symmetric quantum channel is composed of a two-qubit partially entangled state and a three-qubit partially entangled state, where partially entangled Greenberger–Horne–Zeilinger (GHZ state and W state are considered, respectively. All schemes are presented in detail and the unitary operations required are given in concise formulas. Methods are provided for reducing classical communication cost and combining operations to simplify the manipulation. Moreover, our schemes are flexible and applicable in different situations.

  15. Quantum computation

    International Nuclear Information System (INIS)

    Deutsch, D.

    1992-01-01

    As computers become ever more complex, they inevitably become smaller. This leads to a need for components which are fabricated and operate on increasingly smaller size scales. Quantum theory is already taken into account in microelectronics design. This article explores how quantum theory will need to be incorporated into computers in future in order to give them their components functionality. Computation tasks which depend on quantum effects will become possible. Physicists may have to reconsider their perspective on computation in the light of understanding developed in connection with universal quantum computers. (UK)

  16. Correlation Functions in Open Quantum-Classical Systems

    OpenAIRE

    Hsieh, Chang-Yu; Kapral, Raymond

    2013-01-01

    Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is diff...

  17. Quantum Bit Commitment and the Reality of the Quantum State

    Science.gov (United States)

    Srikanth, R.

    2018-01-01

    Quantum bit commitment is insecure in the standard non-relativistic quantum cryptographic framework, essentially because Alice can exploit quantum steering to defer making her commitment. Two assumptions in this framework are that: (a) Alice knows the ensembles of evidence E corresponding to either commitment; and (b) system E is quantum rather than classical. Here, we show how relaxing assumption (a) or (b) can render her malicious steering operation indeterminable or inexistent, respectively. Finally, we present a secure protocol that relaxes both assumptions in a quantum teleportation setting. Without appeal to an ontological framework, we argue that the protocol's security entails the reality of the quantum state, provided retrocausality is excluded.

  18. Post-quantum cryptography

    Science.gov (United States)

    Bernstein, Daniel J.; Lange, Tanja

    2017-09-01

    Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.

  19. Post-quantum cryptography.

    Science.gov (United States)

    Bernstein, Daniel J; Lange, Tanja

    2017-09-13

    Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.

  20. Quantum walk on a chimera graph

    Science.gov (United States)

    Xu, Shu; Sun, Xiangxiang; Wu, Jizhou; Zhang, Wei-Wei; Arshed, Nigum; Sanders, Barry C.

    2018-05-01

    We analyse a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum walk features such as localization that starkly distinguishes classical from quantum behaviour. Motivated by technological thrusts, we study continuous-time quantum walk on enhanced variants of the chimera graph and on diminished chimera graph with a random removal of vertices. We explain the quantum walk by constructing a generating set for a suitable subgroup of graph isomorphisms and corresponding symmetry operators that commute with the quantum walk Hamiltonian; the Hamiltonian and these symmetry operators provide a complete set of labels for the spectrum and the stationary states. Our quantum walk characterization of the chimera graph and its variants yields valuable insights into graphs used for designing quantum-annealers.

  1. Time as a Quantum Observable, Canonically Conjugated to Energy, and Foundations of Self-Consistent Time Analysis of Quantum Processes

    Directory of Open Access Journals (Sweden)

    V. S. Olkhovsky

    2009-01-01

    Full Text Available Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper deals with the maximal Hermitian (but nonself-adjoint operator for time which appears in nonrelativistic quantum mechanics and in quantum electrodynamics for systems with continuous energy spectra and also, briefly, with the four-momentum and four-position operators, for relativistic spin-zero particles. Two measures of averaging over time and connection between them are analyzed. The results of the study of time as a quantum observable in the cases of the discrete energy spectra are also presented, and in this case the quasi-self-adjoint time operator appears. Then, the general foundations of time analysis of quantum processes (collisions and decays are developed on the base of time operator with the proper measures of averaging over time. Finally, some applications of time analysis of quantum processes (concretely, tunneling phenomena and nuclear processes are reviewed.

  2. Quantum walks in brain microtubules--a biomolecular basis for quantum cognition?

    Science.gov (United States)

    Hameroff, Stuart

    2014-01-01

    Cognitive decisions are best described by quantum mathematics. Do quantum information devices operate in the brain? What would they look like? Fuss and Navarro () describe quantum lattice registers in which quantum superpositioned pathways interact (compute/integrate) as 'quantum walks' akin to Feynman's path integral in a lattice (e.g. the 'Feynman quantum chessboard'). Simultaneous alternate pathways eventually reduce (collapse), selecting one particular pathway in a cognitive decision, or choice. This paper describes how quantum walks in a Feynman chessboard are conceptually identical to 'topological qubits' in brain neuronal microtubules, as described in the Penrose-Hameroff 'Orch OR' theory of consciousness. Copyright © 2013 Cognitive Science Society, Inc.

  3. Shuffling cards, factoring numbers and the quantum baker's map

    International Nuclear Information System (INIS)

    Lakshminarayan, Arul

    2005-01-01

    It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of this operator the eigenfunctions of the quantum baker's map are compressed by factors of around five or more. We show explicitly its connection to an operator that is closely related to the usual quantum baker's map. This permutation operator has interesting connections to the art of shuffling cards as well as to the quantum factoring algorithm of Shor via the quantum order finding one. Hence we point out that this well-known quantum algorithm makes crucial use of a quantum chaotic operator, or at least one that is close to the quantization of the left-shift, a closeness that we also explore quantitatively. (letter to the editor)

  4. Bound on quantum computation time: Quantum error correction in a critical environment

    International Nuclear Information System (INIS)

    Novais, E.; Mucciolo, Eduardo R.; Baranger, Harold U.

    2010-01-01

    We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user.

  5. Hybrid quantum-classical modeling of quantum dot devices

    Science.gov (United States)

    Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas

    2017-11-01

    The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

  6. Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

    Science.gov (United States)

    Lin, Cheng-Ju; Motrunich, Olexei I.

    2017-12-01

    We numerically construct translationally invariant quasiconserved operators with maximum range M , which best commute with a nonintegrable quantum spin chain Hamiltonian, up to M =12 . In the large coupling limit, we find that the residual norm of the commutator of the quasiconserved operator decays exponentially with its maximum range M at small M , and turns into a slower decay at larger M . This quasiconserved operator can be understood as a dressed total "spin-z " operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows an almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasiconserved operator.

  7. Quantum control in infinite dimensions

    International Nuclear Information System (INIS)

    Karwowski, Witold; Vilela Mendes, R.

    2004-01-01

    Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite-dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators

  8. Gossip algorithms in quantum networks

    Science.gov (United States)

    Siomau, Michael

    2017-01-01

    Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip algorithms to quantum networks and show that any quantum network can be updated to optimal configuration with local operations and classical communication. This allows to speed-up - in the best case exponentially - the quantum information dissemination. Irrespective of the initial configuration of the quantum network, the update requiters at most polynomial number of local operations and classical communication.

  9. Dynamics of Quantum Causal Structures

    Science.gov (United States)

    Castro-Ruiz, Esteban; Giacomini, Flaminia; Brukner, Časlav

    2018-01-01

    It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, because of quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laboratories is not definite (e.g., one cannot say whether operation in laboratory A occurs before or after operation in laboratory B ). Here, we develop a framework for "dynamics of causal structures," i.e., for transformations of process matrices into process matrices. We show that, under continuous and reversible transformations, the causal order between operations is always preserved. However, the causal order between a subset of operations can be changed under continuous yet nonreversible transformations. An explicit example is that of the quantum switch, where a party in the past affects the causal order of operations of future parties, leading to a transition from a channel from A to B , via superposition of causal orders, to a channel from B to A . We generalize our framework to construct a hierarchy of quantum maps based on transformations of process matrices and transformations thereof.

  10. Concatenated quantum codes

    Energy Technology Data Exchange (ETDEWEB)

    Knill, E.; Laflamme, R.

    1996-07-01

    One main problem for the future of practial quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories and quantum channels require gates with asymptotically zero error to store or transmit an input quantum state for arbitrarily long times or distances with fixed error. This report gives a method which has the property that to store or transmit a qubit with maximum error {epsilon} requires gates with errors at most {ital c}{epsilon} and storage or channel elements with error at most {epsilon}, independent of how long we wish to store the state or how far we wish to transmit it. The method relies on using concatenated quantum codes and hierarchically implemented recovery operations. The overhead of the method is polynomial in the time of storage or the distance of the transmission. Rigorous and heuristic lower bounds for the constant {ital c} are given.

  11. Quantum computers: Definition and implementations

    International Nuclear Information System (INIS)

    Perez-Delgado, Carlos A.; Kok, Pieter

    2011-01-01

    The DiVincenzo criteria for implementing a quantum computer have been seminal in focusing both experimental and theoretical research in quantum-information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. Therefore, the question is what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that, according to this definition, a device is a quantum computer if it obeys the following criteria: Any quantum computer must consist of a quantum memory, with an additional structure that (1) facilitates a controlled quantum evolution of the quantum memory; (2) includes a method for information theoretic cooling of the memory; and (3) provides a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault tolerantly. We discuss various existing quantum computing paradigms and how they fit within this framework. Finally, we present a decision tree for selecting an avenue toward building a quantum computer. This is intended to help experimentalists determine the most natural paradigm given a particular physical implementation.

  12. Intermediate spectral theory and quantum dynamics

    CERN Document Server

    de Oliveira, Cesar R

    2008-01-01

    The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. The book places emphasis on the symbiotic relationship of these two domains by (1) presenting the basic mathematics of nonrelativistic quantum mechanics of one particle, i.e., developing the spectral theory of self-adjoint operators in infinite-dimensional Hilbert spaces from the beginning, and (2) giving an overview of many of the basic functional aspects of quantum theory, from its physical principles to the mathematical models. The book is intended for graduate (or advanced undergraduate) students and researchers interested in mathematical physics. It starts with linear operator theory, spectral questions and self-...

  13. What are quantum jumps?

    International Nuclear Information System (INIS)

    Cook, R.J.

    1988-01-01

    This paper answers the title question by giving an operational definition of quantum jumps based on measurement theory. This definition forms the basis of a theory of quantum jumps which leads to a number of testable predictions. Experiments are proposed to test the theory. The suggested experiments also test the quantum Zeno paradox, i.e., they test the proposition that frequent observation of a quantum system inhibits quantum jumps in that system. (orig.)

  14. A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode.

    Science.gov (United States)

    Kuhlmann, Andreas V; Houel, Julien; Brunner, Daniel; Ludwig, Arne; Reuter, Dirk; Wieck, Andreas D; Warburton, Richard J

    2013-07-01

    Optically active quantum dots, for instance self-assembled InGaAs quantum dots, are potentially excellent single photon sources. The fidelity of the single photons is much improved using resonant rather than non-resonant excitation. With resonant excitation, the challenge is to distinguish between resonance fluorescence and scattered laser light. We have met this challenge by creating a polarization-based dark-field microscope to measure the resonance fluorescence from a single quantum dot at low temperature. We achieve a suppression of the scattered laser exceeding a factor of 10(7) and background-free detection of resonance fluorescence. The same optical setup operates over the entire quantum dot emission range (920-980 nm) and also in high magnetic fields. The major development is the outstanding long-term stability: once the dark-field point has been established, the microscope operates for days without alignment. The mechanical and optical designs of the microscope are presented, as well as exemplary resonance fluorescence spectroscopy results on individual quantum dots to underline the microscope's excellent performance.

  15. A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode

    International Nuclear Information System (INIS)

    Kuhlmann, Andreas V.; Houel, Julien; Warburton, Richard J.; Brunner, Daniel; Ludwig, Arne; Reuter, Dirk; Wieck, Andreas D.

    2013-01-01

    Optically active quantum dots, for instance self-assembled InGaAs quantum dots, are potentially excellent single photon sources. The fidelity of the single photons is much improved using resonant rather than non-resonant excitation. With resonant excitation, the challenge is to distinguish between resonance fluorescence and scattered laser light. We have met this challenge by creating a polarization-based dark-field microscope to measure the resonance fluorescence from a single quantum dot at low temperature. We achieve a suppression of the scattered laser exceeding a factor of 10 7 and background-free detection of resonance fluorescence. The same optical setup operates over the entire quantum dot emission range (920–980 nm) and also in high magnetic fields. The major development is the outstanding long-term stability: once the dark-field point has been established, the microscope operates for days without alignment. The mechanical and optical designs of the microscope are presented, as well as exemplary resonance fluorescence spectroscopy results on individual quantum dots to underline the microscope's excellent performance

  16. A gravitational wave detector operating beyond the quantum shot-noise limit: Squeezed light in application

    Directory of Open Access Journals (Sweden)

    Schnabel Roman

    2013-08-01

    Full Text Available This contribution reviews our recent progress on the generation of squeezed light [1], and also the recent squeezed-light enhancement of the gravitational wave detector GEO 600 [2]. GEO 600 is currently the only GW observatory operated by the LIGO Scientific Collaboration in its search for gravitational waves. With the help of squeezed states of light it now operates with its best ever sensitivity, which not only proves the qualification of squeezed light as a key technology for future gravitational wave astronomy but also the usefulness of quantum entanglement.

  17. Remote interactions on two distributed quantum systems: nonlocal unambiguous quantum-state discrimination

    International Nuclear Information System (INIS)

    Chen Libing; Jin Ruibo; Lu Hong

    2008-01-01

    Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement (POVM). We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM

  18. Conditional quantum entropy power inequality for d-level quantum systems

    Science.gov (United States)

    Jeong, Kabgyun; Lee, Soojoon; Jeong, Hyunseok

    2018-04-01

    We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert et al (2016 J. Math. Phys. 57 052202). Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.

  19. Function Package for Computing Quantum Resource Measures

    Science.gov (United States)

    Huang, Zhiming

    2018-05-01

    In this paper, we present a function package for to calculate quantum resource measures and dynamics of open systems. Our package includes common operators and operator lists, frequently-used functions for computing quantum entanglement, quantum correlation, quantum coherence, quantum Fisher information and dynamics in noisy environments. We briefly explain the functions of the package and illustrate how to use the package with several typical examples. We expect that this package is a useful tool for future research and education.

  20. Quantum mechanics

    International Nuclear Information System (INIS)

    Basdevant, J.L.; Dalibard, J.; Joffre, M.

    2008-01-01

    All physics is quantum from elementary particles to stars and to the big-bang via semi-conductors and chemistry. This theory is very subtle and we are not able to explain it without the help of mathematic tools. This book presents the principles of quantum mechanics and describes its mathematical formalism (wave function, Schroedinger equation, quantum operators, spin, Hamiltonians, collisions,..). We find numerous applications in the fields of new technologies (maser, quantum computer, cryptography,..) and in astrophysics. A series of about 90 exercises with their answers is included. This book is based on a physics course at a graduate level. (A.C.)

  1. Quantum Phonon Optics: Squeezing Quantum Noise in the Atomic Displacements.

    Science.gov (United States)

    Hu, X.; Nori, F.

    1996-03-01

    We have investigated(X. Hu and F. Nori, Physical Review B, in press; preprints.) coherent and squeezed quantum states of phonons. Squeezed states are interesting because they allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of phonon vacuum states. We have studiedfootnotemark[1] the possibility of squeezing quantum noise in the atomic displacement using a polariton-based approach and also a method based on the three-phonon anharmonic interaction. Our focus here is on the first approach. We have diagonalized the polariton Hamiltonian and calculated the corresponding expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators (the later is the phonon analog of the electric field operator for photons). Our results shows that squeezing of quantum fluctuations in the atomic displacements can be achieved with appropriate initial states of both photon and phonon fields. The degree of squeezing is directly related to the crystal susceptibility, which is indicative of the interaction strength between the incident light and the crystal.

  2. Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer

    International Nuclear Information System (INIS)

    Moll, Nikolaj; Fuhrer, Andreas; Staar, Peter; Tavernelli, Ivano

    2016-01-01

    Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the Fermionic problem in a system of qubits. By exploiting the block diagonality of a Fermionic Hamiltonian, we show that the number of required qubits can be reduced while the number of terms in the Hamiltonian will increase. All operations for this reduction can be performed in operator space. The scheme is conceived as a pre-computational step that would be performed prior to the actual quantum simulation. We apply this scheme to reduce the number of qubits necessary to simulate both the Hamiltonian of the two-site Fermi–Hubbard model and the hydrogen molecule. Both quantum systems can then be simulated with a two-qubit quantum computer. Despite the increase in the number of Hamiltonian terms, the scheme still remains a useful tool to reduce the dimensionality of specific quantum systems for quantum simulators with a limited number of resources. (paper)

  3. Quantum ratchets

    OpenAIRE

    Grifoni, Milena

    1997-01-01

    In this thesis, ratchet systems operating in the quantum regime are investigated. Ratchet systems, also known as Brownian motors, are periodic systems presenting an intrinsic asymmetry which can be exploited to extract work out of unbiased forces. As a model for ratchet systems, we consider the motion of a particle in a one-dimensional periodic and asymmetric potential, interacting with a thermal environment, and subject to an unbiased driving force. In quantum ratchets, intrinsic quantum flu...

  4. Detecting a set of entanglement measures in an unknown tripartite quantum state by local operations and classical communication

    International Nuclear Information System (INIS)

    Bai Yankui; Li Shushen; Zheng Houzhi; Wang, Z. D.

    2006-01-01

    We propose a more general method for detecting a set of entanglement measures, i.e., negativities, in an arbitrary tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers do not need to perform partial transposition maps by the structural physical approximation; instead, they only need to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state

  5. Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

    Science.gov (United States)

    Greene, Samuel M; Batista, Victor S

    2017-09-12

    We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

  6. Experimental quantum Hamiltonian learning

    NARCIS (Netherlands)

    Wang, J.; Paesani, S.; Santagati, R.; Knauer, S.; Gentile, A.A.; Wiebe, N.; Petruzzella, M.; O’Brien, J.L.; Rarity, J.G.; Laing, A.; Thompson, M.G.

    2017-01-01

    The efficient characterization of quantum systems1, 2, 3, the verification of the operations of quantum devices4, 5, 6 and the validation of underpinning physical models7, 8, 9, are central challenges for quantum technologies10, 11, 12 and fundamental physics13, 14. The computational cost of such

  7. Nonadiabatic corrections to a quantum dot quantum computer ...

    Indian Academy of Sciences (India)

    2014-07-02

    Jul 2, 2014 ... corrections in it. If the decoherence times of a quantum dot computer are ∼100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be >1010.

  8. Bicovariant quantum algebras and quantum Lie algebras

    International Nuclear Information System (INIS)

    Schupp, P.; Watts, P.; Zumino, B.

    1993-01-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

  9. Quantum spacetime

    International Nuclear Information System (INIS)

    Doplicher, S.

    1996-01-01

    We review some recent result and work in progress on the quantum structure of spacetime at scales comparable with the Planck length; the models discussed here are operationally motivated by the limitations in the accuracy of localization of events in spacetime imposed by the interplay between quantum mechanics and classical general relativity. (orig.)

  10. Quantum-statistical kinetic equations

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

  11. Robustness of holonomic quantum gates

    International Nuclear Information System (INIS)

    Solinas, P.; Zanardi, P.; Zanghi, N.

    2005-01-01

    Full text: If the driving field fluctuates during the quantum evolution this produces errors in the applied operator. The holonomic (and geometrical) quantum gates are believed to be robust against some kind of noise. Because of the geometrical dependence of the holonomic operators can be robust against this kind of noise; in fact if the fluctuations are fast enough they cancel out leaving the final operator unchanged. I present the numerical studies of holonomic quantum gates subject to this parametric noise, the fidelity of the noise and ideal evolution is calculated for different noise correlation times. The holonomic quantum gates seem robust not only for fast fluctuating fields but also for slow fluctuating fields. These results can be explained as due to the geometrical feature of the holonomic operator: for fast fluctuating fields the fluctuations are canceled out, for slow fluctuating fields the fluctuations do not perturb the loop in the parameter space. (author)

  12. Self-assembled quantum dot structures in a hexagonal nanowire for quantum photonics.

    Science.gov (United States)

    Yu, Ying; Dou, Xiu-Ming; Wei, Bin; Zha, Guo-Wei; Shang, Xiang-Jun; Wang, Li; Su, Dan; Xu, Jian-Xing; Wang, Hai-Yan; Ni, Hai-Qiao; Sun, Bao-Quan; Ji, Yuan; Han, Xiao-Dong; Niu, Zhi-Chuan

    2014-05-01

    Two types of quantum nanostructures based on self-assembled GaAs quantumdots embedded into GaAs/AlGaAs hexagonal nanowire systems are reported, opening a new avenue to the fabrication of highly efficient single-photon sources, as well as the design of novel quantum optics experiments and robust quantum optoelectronic devices operating at higher temperature, which are required for practical quantum photonics applications. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  13. The quantum symmetry of rational conformal field theories

    Directory of Open Access Journals (Sweden)

    César Gómez

    1991-04-01

    Full Text Available The quantum group symmetry of the c ˇ1 Rational Conformal Field Theory, in its Coulomb gas version, is formulated in terms of a new type of screened vertex operators, which define the representation spaces of a quantum group Q. The conformal properties of these operators show a deep interplay between the quantum group Q and the Virasoro algebra.The R-matrix, the comultiplication rules and the quantum Clebsch-Gordan coefficients of Q are obtained using contour deformation techniques. Finally, the relation between the chiral vertex operators and the quantum Clebsch-Gordan coefficients is shown.

  14. Virtual Quantum Subsystems

    International Nuclear Information System (INIS)

    Zanardi, Paolo

    2001-01-01

    The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables. The algebraic structure of A selects a preferred tensor product structure, i.e., a partition into subsystems. The notion of compoundness for quantum systems is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomies

  15. Dynamics of Quantum Causal Structures

    Directory of Open Access Journals (Sweden)

    Esteban Castro-Ruiz

    2018-03-01

    Full Text Available It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, because of quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laboratories is not definite (e.g., one cannot say whether operation in laboratory A occurs before or after operation in laboratory B. Here, we develop a framework for “dynamics of causal structures,” i.e., for transformations of process matrices into process matrices. We show that, under continuous and reversible transformations, the causal order between operations is always preserved. However, the causal order between a subset of operations can be changed under continuous yet nonreversible transformations. An explicit example is that of the quantum switch, where a party in the past affects the causal order of operations of future parties, leading to a transition from a channel from A to B, via superposition of causal orders, to a channel from B to A. We generalize our framework to construct a hierarchy of quantum maps based on transformations of process matrices and transformations thereof.

  16. Quantum games in open systems using biophysical Hamiltonians

    International Nuclear Information System (INIS)

    Faber, Jean; Portugal, Renato; Rosa, Luiz Pinguelli

    2006-01-01

    We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information

  17. Quantum games in open systems using biophysical Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Faber, Jean [National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Quitandinha 25651-075, Petropolis, RJ (Brazil)]. E-mail: faber@lncc.br; Portugal, Renato [National Laboratory of Scientific Computing (LNCC), Av. Getulio Vargas 333, Quitandinha 25651-075, Petropolis, RJ (Brazil)]. E-mail: portugal@lncc.br; Rosa, Luiz Pinguelli [Federal University of Rio de Janeiro, COPPE-UFRJ, RJ (Brazil)]. E-mail: lpr@adc.coppe.ufrj.br

    2006-09-25

    We analyze the necessary physical conditions to model an open quantum system as a quantum game. By applying the formalism of quantum operations on a particular system, we use Kraus operators as quantum strategies. The physical interpretation is a conflict among different configurations of the environment. The resolution of the conflict displays regimes of minimum loss of information.

  18. Quantum chaos in the Heisenberg picture

    International Nuclear Information System (INIS)

    McKellar, B.H.J.; Lancaster, M.; McCaw, J.

    2000-01-01

    Full text: We explore the possibility of defining quantum chaos in the algebra of quantum mechanical operators. The simple definition of the Lyapunov exponent in terms of a metric on that algebra has the expected properties for the quantum logistic map, as we confirm for the simple spin 1 system. We then show numerically and analytically that the Hamiltonian evolution of finite spin systems does not lead to chaos in this definition, and investigate alternative definitions of quantum chaos in the algebra of operators

  19. One-Way Quantum Authenticated Secure Communication Using Rotation Operation

    International Nuclear Information System (INIS)

    Tsai Chia-Wei; Wei Toung-Shang; Hwang Tzonelih

    2011-01-01

    This study proposes a theoretical quantum authenticated secure communication (QASC) protocol using Einstein-Podolsky-Rosen (EPR) entangle state, which enables a sender to send a secure as well as authenticated message to a receiver within only one step quantum transmission without having the classical channels and the certification authority. (general)

  20. Rabi model as a quantum coherent heat engine: From quantum biology to superconducting circuits

    Science.gov (United States)

    Altintas, Ferdi; Hardal, Ali Ü. C.; Müstecaplıoǧlu, Özgür E.

    2015-02-01

    We propose a multilevel quantum heat engine with a working medium described by a generalized Rabi model which consists of a two-level system coupled to a single-mode bosonic field. The model is constructed to be a continuum limit of a quantum biological description of light-harvesting complexes so that it can amplify quantum coherence by a mechanism which is a quantum analog of classical Huygens clocks. The engine operates in a quantum Otto cycle where the working medium is coupled to classical heat baths in the isochoric processes of the four-stroke cycle, while either the coupling strength or the resonance frequency is changed in the adiabatic stages. We found that such an engine can produce work with an efficiency close to the Carnot bound when it operates at low temperatures and in the ultrastrong-coupling regime. The interplay of the effects of quantum coherence and quantum correlations on the engine performance is discussed in terms of second-order coherence, quantum mutual information, and the logarithmic negativity of entanglement. We point out that the proposed quantum Otto engine can be implemented experimentally with modern circuit quantum electrodynamic systems where flux qubits can be coupled ultrastrongly to superconducting transmission-line resonators.

  1. On Spectral Triples in Quantum Gravity I

    DEFF Research Database (Denmark)

    Aastrup, Johannes; M. Grimstrup, Jesper; Nest, Ryszard

    2009-01-01

    This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator....... The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly......, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations...

  2. Engineering quantum mechanics

    CERN Document Server

    Ahn, Doyeol

    2011-01-01

    A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...

  3. Pseudospectra in non-Hermitian quantum mechanics

    Science.gov (United States)

    Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

    2015-10-01

    We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

  4. Quantum neurophysics: From non-living matter to quantum neurobiology and psychopathology.

    Science.gov (United States)

    Tarlacı, Sultan; Pregnolato, Massimo

    2016-05-01

    The concepts of quantum brain, quantum mind and quantum consciousness have been increasingly gaining currency in recent years, both in scientific papers and in the popular press. In fact, the concept of the quantum brain is a general framework. Included in it are basically four main sub-headings. These are often incorrectly used interchangeably. The first of these and the one which started the quantum mind/consciousness debate was the place of consciousness in the problem of measurement in quantum mechanics. Debate on the problem of quantum measurement and about the place of the conscious observer has lasted almost a century. One solution to this problem is that the participation of a conscious observer in the experiment will radically change our understanding of the universe and our relationship with the outside world. The second topic is that of quantum biology. This topic has become a popular field of research, especially in the last decade. It concerns whether or not the rules of quantum physics operate in biological structures. It has been shown in the latest research on photosynthesis, the sense of smell and magnetic direction finding in animals that the laws of quantum physics may operate in warm-wet-noisy biological structures. The third sub-heading is quantum neurobiology. This topic has not yet gained wide acceptance and is still in its early stages. Its primary purpose is directed to understand whether the laws of quantum physics are effective in the biology of the nervous system or not. A further step in brain neurobiology, toward the understanding of consciousness formation, is the research of quantum laws effects upon neural network functions. The fourth and final topic is quantum psychopathology. This topic takes its basis and its support from quantum neurobiology. It comes from the idea that if quantum physics is involved in the normal working of the brain, diseased conditions of the brain such as depression, anxiety, dementia, schizophrenia and

  5. Topics in linear optical quantum computation

    Science.gov (United States)

    Glancy, Scott Charles

    This thesis covers several topics in optical quantum computation. A quantum computer is a computational device which is able to manipulate information by performing unitary operations on some physical system whose state can be described as a vector (or mixture of vectors) in a Hilbert space. The basic unit of information, called the qubit, is considered to be a system with two orthogonal states, which are assigned logical values of 0 and 1. Photons make excellent candidates to serve as qubits. They have little interactions with the environment. Many operations can be performed using very simple linear optical devices such as beam splitters and phase shifters. Photons can easily be processed through circuit-like networks. Operations can be performed in very short times. Photons are ideally suited for the long-distance communication of quantum information. The great difficulty in constructing an optical quantum computer is that photons naturally interact weakly with one another. This thesis first gives a brief review of two early approaches to optical quantum computation. It will describe how any discrete unitary operation can be performed using a single photon and a network of beam splitters, and how the Kerr effect can be used to construct a two photon logic gate. Second, this work provides a thorough introduction to the linear optical quantum computer developed by Knill, Laflamme, and Milburn. It then presents this author's results on the reliability of this scheme when implemented using imperfect photon detectors. This author finds that quantum computers of this sort cannot be built using current technology. Third, this dissertation describes a method for constructing a linear optical quantum computer using nearly orthogonal coherent states of light as the qubits. It shows how a universal set of logic operations can be performed, including calculations of the fidelity with which these operations may be accomplished. It discusses methods for reducing and

  6. Macroscopic and non-linear quantum games

    International Nuclear Information System (INIS)

    Aerts, D.; D'Hooghe, A.; Posiewnik, A.; Pykacz, J.

    2005-01-01

    Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)

  7. A Comparison of Implications in Orthomodular Quantum Logic—Morphological Analysis of Quantum Logic

    Directory of Open Access Journals (Sweden)

    Mitsuhiko Fujio

    2012-01-01

    Full Text Available Morphological operators are generalized to lattices as adjunction pairs (Serra, 1984; Ronse, 1990; Heijmans and Ronse, 1990; Heijmans, 1994. In particular, morphology for set lattices is applied to analyze logics through Kripke semantics (Bloch, 2002; Fujio and Bloch, 2004; Fujio, 2006. For example, a pair of morphological operators as an adjunction gives rise to a temporalization of normal modal logic (Fujio and Bloch, 2004; Fujio, 2006. Also, constructions of models for intuitionistic logic or linear logics can be described in terms of morphological interior and/or closure operators (Fujio and Bloch, 2004. This shows that morphological analysis can be applied to various non-classical logics. On the other hand, quantum logics are algebraically formalized as orhomodular or modular ortho-complemented lattices (Birkhoff and von Neumann, 1936; Maeda, 1980; Chiara and Giuntini, 2002, and shown to allow Kripke semantics (Chiara and Giuntini, 2002. This suggests the possibility of morphological analysis for quantum logics. In this article, to show an efficiency of morphological analysis for quantum logic, we consider the implication problem in quantum logics (Chiara and Giuntini, 2002. We will give a comparison of the 5 polynomial implication connectives available in quantum logics.

  8. Experimental demonstration of selective quantum process tomography on an NMR quantum information processor

    Science.gov (United States)

    Gaikwad, Akshay; Rehal, Diksha; Singh, Amandeep; Arvind, Dorai, Kavita

    2018-02-01

    We present the NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of the quantum process matrix to a desired precision, provided a set of quantum states can be prepared efficiently. Our modified technique requires fewer experimental resources as compared to the standard implementation of selective and efficient quantum process tomography, as it exploits the special nature of NMR measurements to allow us to compute specific elements of the process matrix by a restrictive set of subsystem measurements. To demonstrate the efficacy of our scheme, we experimentally tomograph the processes corresponding to "no operation," a controlled-NOT (CNOT), and a controlled-Hadamard gate on a two-qubit NMR quantum information processor, with high fidelities.

  9. Adiabatic Quantum Computing

    Science.gov (United States)

    Landahl, Andrew

    2012-10-01

    Quantum computers promise to exploit counterintuitive quantum physics principles like superposition, entanglement, and uncertainty to solve problems using fundamentally fewer steps than any conventional computer ever could. The mere possibility of such a device has sharpened our understanding of quantum coherent information, just as lasers did for our understanding of coherent light. The chief obstacle to developing quantum computer technology is decoherence--one of the fastest phenomena in all of physics. In principle, decoherence can be overcome by using clever entangled redundancies in a process called fault-tolerant quantum error correction. However, the quality and scale of technology required to realize this solution appears distant. An exciting alternative is a proposal called ``adiabatic'' quantum computing (AQC), in which adiabatic quantum physics keeps the computer in its lowest-energy configuration throughout its operation, rendering it immune to many decoherence sources. The Adiabatic Quantum Architectures In Ultracold Systems (AQUARIUS) Grand Challenge Project at Sandia seeks to demonstrate this robustness in the laboratory and point a path forward for future hardware development. We are building devices in AQUARIUS that realize the AQC architecture on up to three quantum bits (``qubits'') in two platforms: Cs atoms laser-cooled to below 5 microkelvin and Si quantum dots cryo-cooled to below 100 millikelvin. We are also expanding theoretical frontiers by developing methods for scalable universal AQC in these platforms. We have successfully demonstrated operational qubits in both platforms and have even run modest one-qubit calculations using our Cs device. In the course of reaching our primary proof-of-principle demonstrations, we have developed multiple spinoff technologies including nanofabricated diffractive optical elements that define optical-tweezer trap arrays and atomic-scale Si lithography commensurate with placing individual donor atoms with

  10. Relativistic Quantum Mechanics

    International Nuclear Information System (INIS)

    Antoine, J-P

    2004-01-01

    The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled 'Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic

  11. Coherent control of quantum dots

    DEFF Research Database (Denmark)

    Johansen, Jeppe; Lodahl, Peter; Hvam, Jørn Märcher

    In recent years much effort has been devoted to the use of semiconductor quantum dotsystems as building blocks for solid-state-based quantum logic devices. One importantparameter for such devices is the coherence time, which determines the number ofpossible quantum operations. From earlier...

  12. Quantum Logic Networks for Probabilistic and Controlled Teleportation of Unknown Quantum States

    Institute of Scientific and Technical Information of China (English)

    GAO Ting

    2004-01-01

    We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one particle and two particles and construct efficient quantum logic networks for implementing the new schemes by means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement, and classically controlled operations. In these schemes the teleportation are not always successful but with certain probability.

  13. Quantum mechanics a fundamental approach

    CERN Document Server

    Wan, K Kong

    2018-01-01

    The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning. This makes it difficult to appreciate the mathematical formalism and hampers the understanding of quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. Quantum mechanics is presented in six groups of postulates. A chapter is devoted to each group of postulates with a detailed discussion. Systems with superselection rules, and some conceptual issues such as quantum paradoxes and measurement, are also discussed. The book conc...

  14. Maxwell's equations, quantum physics and the quantum graviton

    International Nuclear Information System (INIS)

    Gersten, Alexander; Moalem, Amnon

    2011-01-01

    Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of 'relativistic quaternions'. Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.

  15. Introduction to quantum information science

    Energy Technology Data Exchange (ETDEWEB)

    Hayashi, Masahito [Nagoya Univ. (Japan). Graduate School of Mathematics; Ishizaka, Satoshi [Hiroshima Univ., Higashi-Hiroshima (Japan). Graduate School of Integrated Arts and Sciences; Kawachi, Akinori [Tokyo Institute of Technology (Japan). Dept. of Mathematical and Computing Sciences; Kimura, Gen [Shibaura Institute of Technology, Saitama (Japan). College of Systems Engineering and Science; Ogawa, Tomohiro [Univ. of Electro-Communications, Tokyo (Japan). Graduate School of Information Systems

    2015-04-01

    Presents the mathematical foundation for quantum information in a very didactic way. Summarizes all required mathematical knowledge in linear algebra. Supports teaching and learning with more than 100 exercises with solutions. Includes brief descriptions to recent results with references. This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols,this book contains quantum teleportation, quantum dense coding, quantum data compression. In particular conversion theory of entanglement via local operation and classical communication are treated too. This theory provides the quantification of entanglement, which coincides with von Neumann entropy. The next part treats the quantum hypothesis testing. The decision problem of two candidates of the unknown state are given. The asymptotic performance of this problem is characterized by information quantities. Using this result, the optimal performance of classical information transmission via noisy quantum channel is derived. Quantum information transmission via noisy quantum channel by quantum error

  16. Introduction to quantum information science

    International Nuclear Information System (INIS)

    Hayashi, Masahito; Ishizaka, Satoshi; Kawachi, Akinori; Kimura, Gen; Ogawa, Tomohiro

    2015-01-01

    Presents the mathematical foundation for quantum information in a very didactic way. Summarizes all required mathematical knowledge in linear algebra. Supports teaching and learning with more than 100 exercises with solutions. Includes brief descriptions to recent results with references. This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols,this book contains quantum teleportation, quantum dense coding, quantum data compression. In particular conversion theory of entanglement via local operation and classical communication are treated too. This theory provides the quantification of entanglement, which coincides with von Neumann entropy. The next part treats the quantum hypothesis testing. The decision problem of two candidates of the unknown state are given. The asymptotic performance of this problem is characterized by information quantities. Using this result, the optimal performance of classical information transmission via noisy quantum channel is derived. Quantum information transmission via noisy quantum channel by quantum error correction are

  17. Quantum groups: Geometry and applications

    International Nuclear Information System (INIS)

    Chu, C.S.

    1996-01-01

    The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge

  18. Non-perturbative description of quantum systems

    CERN Document Server

    Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander

    2015-01-01

    This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory.  In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

  19. On the connection between quantum fields and von Neumann algebras of local operators

    International Nuclear Information System (INIS)

    Driessler, W.; Summers, S.J.; Wichmann, E.H.

    1986-01-01

    The relationship between a standard local quantum field and a net of local von Neumann algebras is discussed. Two natural possibilities for such an association are identified, and conditions for these to obtain are found. It is shown that the local net can naturally be so chosen that it satisfies the Special Condition of Duality. The notion of an intrinsically local field operator is introduced, and it is shown that such an operator defines a local net with which the field is locally associated. A regularity condition on the field is formulated, and it is shown that if this condition holds, then there exists a unique local net with which the field is locally associated if and only if the field algebra contains at least one intrinsically local operator. Conditions under which a field and other fields in its Borchers class are associated with the same local net are found, in terms of the regularity condition mentioned. (orig.)

  20. Metrics of quantum states

    International Nuclear Information System (INIS)

    Ma Zhihao; Chen Jingling

    2011-01-01

    In this work we study metrics of quantum states, which are natural generalizations of the usual trace metric and Bures metric. Some useful properties of the metrics are proved, such as the joint convexity and contractivity under quantum operations. Our result has a potential application in studying the geometry of quantum states as well as the entanglement detection.

  1. Automated searching for quantum subsystem codes

    International Nuclear Information System (INIS)

    Crosswhite, Gregory M.; Bacon, Dave

    2011-01-01

    Quantum error correction allows for faulty quantum systems to behave in an effectively error-free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to active quantum error-correcting schemes as well as to the design of self-correcting quantum memories. Previous approaches for investigating these codes have focused on applying theoretical analysis to look for interesting codes and to investigate their properties. In this paper we present an alternative approach that uses computational analysis to accomplish the same goals. Specifically, we present an algorithm that computes the optimal quantum subsystem code that can be implemented given an arbitrary set of measurement operators that are tensor products of Pauli operators. We then demonstrate the utility of this algorithm by performing a systematic investigation of the quantum subsystem codes that exist in the setting where the interactions are limited to two-body interactions between neighbors on lattices derived from the convex uniform tilings of the plane.

  2. Information theoretic resources in quantum theory

    Science.gov (United States)

    Meznaric, Sebastian

    Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first part of this thesis we quantify the effective entanglement when operations are additionally restricted to account for both fundamental restrictions on operations, such as those arising from superselection rules, as well as experimental errors arising from the imperfections in the apparatus. For an important class of errors we find a linear relationship between the usual and effective higher dimensional generalization of concurrence, a measure of entanglement. Following the treatment of effective entanglement, we focus on a related concept of nonlocality in the presence of superselection rules (SSR). Here we propose a scheme that may be used to activate nongenuinely multipartite nonlocality, in that a single copy of a state is not multipartite nonlocal, while two or more copies exhibit nongenuinely multipartite nonlocality. The states used exhibit the more powerful genuinely multipartite nonlocality when SSR are not enforced, but not when they are, raising the question of what is needed for genuinely multipartite nonlocality. We show that whenever the number of particles is insufficient, the degrading of genuinely multipartite to nongenuinely multipartite nonlocality is necessary. While in the first few chapters we focus our attention on understanding the resources present in quantum states, in the final part we turn the picture around and instead treat operations themselves as a resource. We provide our observers with free access to classical operations - ie. those that cannot detect or generate quantum coherence. We show that the operation of interest can then be used to either generate or detect quantum coherence if and only if it violates a particular commutation relation. Using the relative entropy, the

  3. Research on Palmprint Identification Method Based on Quantum Algorithms

    Directory of Open Access Journals (Sweden)

    Hui Li

    2014-01-01

    Full Text Available Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of N operations to find out the target palmprint, but the traditional method needs N times of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%.

  4. Non-relativistic quantum mechanics

    CERN Document Server

    Puri, Ravinder R

    2017-01-01

    This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...

  5. New foundation of quantum theory

    International Nuclear Information System (INIS)

    Schmutzer, E.

    1976-01-01

    A new foundation of quantum theory is given on the basis of the formulated 'Principle of Fundamental Covariance', combining the 'Principle of General Relativity' (coordinate-covariance in space-time) and the 'Principle of Operator-Covariance' (in Hilbert space). The fundamental quantum laws proposed are: (1) time-dependent simultaneous laws of motion for the operators, general states and eigenstates, (2) commutation relations, (3) time-dependent eigenvalue equations. All these laws fulfill the Principle of Fundamental Covariance (in non-relativistic quantum mechanics with restricted coordinate transformations). (author)

  6. Quantum Processes Which Do Not Use Coherence

    Directory of Open Access Journals (Sweden)

    Benjamin Yadin

    2016-11-01

    Full Text Available A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalization of incoherent operations—those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem, showing how these operations can always be constructed by the system interacting, in an incoherent way, with an ancilla. Such a physical justification is not known for the incoherent operations; thus, our results lead to a physically well-motivated resource theory of coherence. Next, we investigate the implications for coherence in multipartite systems. We show that quantum correlations can be defined naturally with respect to a fixed basis, providing a link between coherence and quantum discord. We demonstrate the interplay between these two quantities in the operations that we study and suggest implications for the theory of quantum discord by relating these operations to those which cannot create discord.

  7. Noninvasive Quantum Measurement of Arbitrary Operator Order by Engineered Non-Markovian Detectors

    Science.gov (United States)

    Bülte, Johannes; Bednorz, Adam; Bruder, Christoph; Belzig, Wolfgang

    2018-04-01

    The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous—detector dynamics-dependent—measurement. A quantum memory effect that we term "system-mediated detector-detector interaction" is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.

  8. A Comparative Study of Quantum and Classical Deletion

    International Nuclear Information System (INIS)

    Shen Yao; Hao Liang; Long Guilu

    2010-01-01

    Here in this letter, we study the difference between quantum and classical deletion. We point out that the linear mapping deletion operation used in the impossibility proof for quantum systems applies also to classical system. The general classical deletion operation is a combined operation of measurement and transformation, i.e., first read the state and then transfer the state to the standard blank state. Though both quantum information and classical information can be deleted in an open system, quantum information cannot be recovered while classical information can be recovered. (general)

  9. On the 'principle of the quantumness', the quantumness of Relativity, and the computational grand-unification

    International Nuclear Information System (INIS)

    D'Ariano, Giacomo Mauro

    2010-01-01

    I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational 'principles of the quantumness', I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm 'the universe is a huge quantum computer', reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.

  10. Quantum mechanics

    CERN Document Server

    Powell, John L

    2015-01-01

    Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ

  11. Threshold quantum state sharing based on entanglement swapping

    Science.gov (United States)

    Qin, Huawang; Tso, Raylin

    2018-06-01

    A threshold quantum state sharing scheme is proposed. The dealer uses the quantum-controlled-not operations to expand the d-dimensional quantum state and then uses the entanglement swapping to distribute the state to a random subset of participants. The participants use the single-particle measurements and unitary operations to recover the initial quantum state. In our scheme, the dealer can share different quantum states among different subsets of participants simultaneously. So the scheme will be very flexible in practice.

  12. Correlation Functions in Open Quantum-Classical Systems

    Directory of Open Access Journals (Sweden)

    Chang-Yu Hsieh

    2013-12-01

    Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.

  13. Introduction to quantum information science

    CERN Document Server

    Hayashi, Masahito; Kawachi, Akinori; Kimura, Gen; Ogawa, Tomohiro

    2015-01-01

    This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current  book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols,this book contains quantum teleport...

  14. Nonlinear optics quantum computing with circuit QED.

    Science.gov (United States)

    Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M

    2013-02-08

    One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.

  15. Channel Simulation in Quantum Metrology

    Directory of Open Access Journals (Sweden)

    Laurenza Riccardo

    2018-04-01

    Full Text Available In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels,wemay express the quantum Cramér Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.

  16. Quantum computing with defects in diamond

    International Nuclear Information System (INIS)

    Jelezko, F.; Gaebel, T.; Popa, I.; Domhan, M.; Wittmann, C.; Wrachtrup, J.

    2005-01-01

    Full text: Single spins in semiconductors, in particular associated with defect centers, are promising candidates for practical and scalable implementation of quantum computing even at room temperature. Such an implementation may also use the reliable and well known gate constructions from bulk nuclear magnetic resonance (NMR) quantum computing. Progress in development of quantum processor based on defects in diamond will be discussed. By combining optical microscopy, and magnetic resonance techniques, the first quantum logical operations on single spins in a solid are now demonstrated. The system is perspective for room temperature operation because of a weak dependence of decoherence on temperature (author)

  17. Almost sharp quantum effects

    International Nuclear Information System (INIS)

    Arias, Alvaro; Gudder, Stan

    2004-01-01

    Quantum effects are represented by operators on a Hilbert space satisfying 0≤A≤I, and sharp quantum effects are represented by projection operators. We say that an effect A is almost sharp if A=PQP for projections P and Q. We give simple characterizations of almost sharp effects. We also characterize effects that can be written as longer products of projections. For generality we first work in the formalism of von Neumann algebras. We then specialize to the full operator algebra B(H) and to finite dimensional Hilbert spaces

  18. Autonomous quantum Maxwell's demon based on two exchange-coupled quantum dots

    Science.gov (United States)

    Ptaszyński, Krzysztof

    2018-01-01

    I study an autonomous quantum Maxwell's demon based on two exchange-coupled quantum dots attached to the spin-polarized leads. The principle of operation of the demon is based on the coherent oscillations between the spin states of the system which act as a quantum iSWAP gate. Due to the operation of the iSWAP gate, one of the dots acts as a feedback controller which blocks the transport with the bias in the other dot, thus inducing the electron pumping against the bias; this leads to the locally negative entropy production. Operation of the demon is associated with the information transfer between the dots, which is studied quantitatively by mapping the analyzed setup onto the thermodynamically equivalent auxiliary system. The calculated entropy production in a single subsystem and information flow between the subsystems are shown to obey a local form of the second law of thermodynamics, similar to the one previously derived for classical bipartite systems.

  19. A relational solution to the problem of time in quantum mechanics and quantum gravity: a fundamental mechanism for quantum decoherence

    International Nuclear Information System (INIS)

    Gambini, Rodolfo; Porto, Rafael A; Pullin, Jorge

    2004-01-01

    The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a 'clock'. Conditional probabilities are computed for variables of the system to take certain values when the 'clock' specifies a certain time. This framework is attractive in contexts where the assumption of usual quantum mechanics of the existence of an external, perfectly classical clock, appears unnatural, as in quantum cosmology. Until recently, there were problems with such constructions in ordinary quantum mechanics with additional difficulties in the context of constrained theories like general relativity. A scheme we recently introduced to consistently discretize general relativity removed such obstacles. Since the clock is now an object subject to quantum fluctuations, the resulting evolution in time is not exactly unitary and pure states decohere into mixed states. Here we work out in detail the type of decoherence generated, and we find it to be of Lindblad type. This is attractive since it implies that one can have loss of coherence without violating the conservation of energy. We apply the framework to a simple cosmological model to illustrate how a quantitative estimate of the effect could be computed. For most quantum systems it appears to be too small to be observed, although certain macroscopic quantum systems could in the future provide a testing ground for experimental observation

  20. Design of quaternary logic circuit using quantum dot gate-quantum dot channel FET (QDG-QDCFET)

    Science.gov (United States)

    Karmakar, Supriya

    2014-10-01

    This paper presents the implementation of quaternary logic circuits based on quantum dot gate-quantum dot channel field effect transistor (QDG-QDCFET). The super lattice structure in the quantum dot channel region of QDG-QDCFET and the electron tunnelling from inversion channel to the quantum dot layer in the gate region of a QDG-QDCFET change the threshold voltage of this device which produces two intermediate states between its ON and OFF states. This property of QDG-QDCFET is used to implement multi-valued logic for future multi-valued logic circuit. This paper presents the design of basic quaternary logic operation such as inverter, AND and OR operation based on QDG-QDCFET.

  1. Quantum memory Quantum memory

    Science.gov (United States)

    Le Gouët, Jean-Louis; Moiseev, Sergey

    2012-06-01

    quest for higher efficiency, better fidelity, broader bandwidth, multimode capacity and longer storage lifetime is pursued in all those approaches, as shown in this special issue. The improvement of quantum memory operation specifically requires in-depth study and control of numerous physical processes leading to atomic decoherence. The present issue reflects the development of rare earth ion doped matrices offering long lifetime superposition states, either as bulk crystals or as optical waveguides. The need for quantum sources and high efficiency detectors at the single photon level is also illustrated. Several papers address the networking of quantum memories either in long-haul cryptography or in the prospect of quantum processing. In this context, much attention has been paid recently to interfacing quantum light with superconducting qubits and with nitrogen-vacancy centers in diamond. Finally, the quantum interfacing of light with matter raises questions on entanglement. The last two papers are devoted to the generation of entanglement by dissipative processes. It is shown that long lifetime entanglement may be built in this way. We hope this special issue will help readers to become familiar with the exciting field of ensemble-based quantum memories and will stimulate them to bring deeper insights and new ideas to this area.

  2. Testing Nonassociative Quantum Mechanics.

    Science.gov (United States)

    Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

    2015-11-27

    The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

  3. An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

    International Nuclear Information System (INIS)

    Arcos-Olalla, Rafael; Reyes, Marco A.; Rosu, Haret C.

    2012-01-01

    We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.

  4. An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

    Energy Technology Data Exchange (ETDEWEB)

    Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)

    2012-10-01

    We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.

  5. Quantum control with NMR methods: Application to quantum simulations

    International Nuclear Information System (INIS)

    Negrevergne, Camille

    2002-01-01

    Manipulating information according to quantum laws allows improvements in the efficiency of the way we treat certain problems. Liquid state Nuclear Magnetic Resonance methods allow us to initialize, manipulate and read the quantum state of a system of coupled spins. These methods have been used to realize an experimental small Quantum Information Processor (QIP) able to process information through around hundred elementary operations. One of the main themes of this work was to design, optimize and validate reliable RF-pulse sequences used to 'program' the QIP. Such techniques have been used to run a quantum simulation algorithm for anionic systems. Some experimental results have been obtained on the determination of Eigen energies and correlation function for a toy problem consisting of fermions on a lattice, showing an experimental proof of principle for such quantum simulations. (author) [fr

  6. Quantum theory informational foundations and foils

    CERN Document Server

    Spekkens, Robert

    2016-01-01

    This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information.  Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quant...

  7. Analytical solutions for quantum walks on 1D chain with different shift operators

    International Nuclear Information System (INIS)

    Xu, Xin-Ping; Zhang, Xiao-Kun; Ide, Yusuke; Konno, Norio

    2014-01-01

    In this paper, we study the discrete-time quantum walks on 1D Chain with the moving and swapping shift operators. We derive analytical solutions for the eigenvalues and eigenstates of the evolution operator U -hat using the Chebyshev polynomial technique, and calculate the long-time averaged probabilities for the two different shift operators respectively. It is found that the probability distributions for the moving and swapping shift operators display completely different characteristics. For the moving shift operator, the probability distribution exhibits high symmetry where the probabilities at mirror positions are equal. The probabilities are inversely proportional to the system size N and approach to zero as N→∞. On the contrary, for the swapping shift operator, the probability distribution is not symmetric, the probability distribution approaches to a power-law stationary distribution as N→∞ under certain coin parameter condition. We show that such power-law stationary distribution is determined by the eigenstates of the eigenvalues ±1 and calculate the intrinsic probability for different starting positions. Our findings suggest that the eigenstates corresponding to eigenvalues ±1 play an important role for the swapping shift operator. - Highlights: • QWs on 1D chain with the moving and swapping operators are studied for the first time. • We derive analytical results for the probability distribution for the two operators. •We compare the dynamics of QWs with two different shift operators. • We find the particular eigenvalues ±1 play an important role for the dynamics. • We use the Chebyshev technique to treat the problem

  8. Quantum principles and particles

    CERN Document Server

    Wilcox, Walter

    2012-01-01

    QUANTUM PRINCIPLESPerspective and PrinciplesPrelude to Quantum MechanicsStern-Gerlach Experiment Idealized Stern-Gerlach ResultsClassical Model AttemptsWave Functions for Two Physical-Outcome CaseProcess Diagrams, Operators, and Completeness Further Properties of Operators/ModulationOperator ReformulationOperator RotationBra-Ket Notation/Basis StatesTransition AmplitudesThree-Magnet Setup Example-CoherenceHermitian ConjugationUnitary OperatorsA Very Special OperatorMatrix RepresentationsMatrix Wave Function RecoveryExpectation ValuesWrap Up ProblemsFree Particles in One DimensionPhotoelectric EffectCompton EffectUncertainty Relation for PhotonsStability of Ground StatesBohr ModelFourier Transform and Uncertainty RelationsSchrödinger EquationSchrödinger Equation ExampleDirac Delta FunctionsWave Functions and ProbabilityProbability CurrentTime Separable SolutionsCompleteness for Particle StatesParticle Operator PropertiesOperator RulesTime Evolution and Expectation ValuesWrap-UpProblemsSome One-Dimensional So...

  9. Quantum computing with black-box quantum subroutines

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, Jayne [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore (Singapore); Gu, Mile [Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing (China); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore (Singapore); Modi, Kavan [School of Physics, Monash University, Clayton, Victoria 3800 (Australia); Vedral, Vlatko [Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore (Singapore)

    2014-07-01

    In classical computation a subroutine is treated as a black box and we do not need to know its exact physical implementation to use it. A complex problem can be decomposed into smaller problems using such modularity. We show that quantum mechanically applying an unknown quantum process as a subroutine is impossible, and this restricts computation models such as DQC1 from operating on unknown inputs. We present a method to avoid this situation for certain computational problems and apply to a modular version of Shor's factoring algorithm. We examine how quantum entanglement and discord fare in this implementation. In this way we are able to study the role of discord in Shor's factoring algorithm.

  10. Anomaly freedom in perturbative loop quantum gravity

    International Nuclear Information System (INIS)

    Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.

    2008-01-01

    A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, nontrivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.

  11. Unconditional polarization qubit quantum memory at room temperature

    Science.gov (United States)

    Namazi, Mehdi; Kupchak, Connor; Jordaan, Bertus; Shahrokhshahi, Reihaneh; Figueroa, Eden

    2016-05-01

    The creation of global quantum key distribution and quantum communication networks requires multiple operational quantum memories. Achieving a considerable reduction in experimental and cost overhead in these implementations is thus a major challenge. Here we present a polarization qubit quantum memory fully-operational at 330K, an unheard frontier in the development of useful qubit quantum technology. This result is achieved through extensive study of how optical response of cold atomic medium is transformed by the motion of atoms at room temperature leading to an optimal characterization of room temperature quantum light-matter interfaces. Our quantum memory shows an average fidelity of 86.6 +/- 0.6% for optical pulses containing on average 1 photon per pulse, thereby defeating any classical strategy exploiting the non-unitary character of the memory efficiency. Our system significantly decreases the technological overhead required to achieve quantum memory operation and will serve as a building block for scalable and technologically simpler many-memory quantum machines. The work was supported by the US-Navy Office of Naval Research, Grant Number N00141410801 and the Simons Foundation, Grant Number SBF241180. B. J. acknowledges financial assistance of the National Research Foundation (NRF) of South Africa.

  12. Quantum computing and spintronics

    International Nuclear Information System (INIS)

    Kantser, V.

    2007-01-01

    Tentative to build a computer, which can operate according to the quantum laws, has leaded to concept of quantum computing algorithms and hardware. In this review we highlight recent developments which point the way to quantum computing on the basis solid state nanostructures after some general considerations concerning quantum information science and introducing a set of basic requirements for any quantum computer proposal. One of the major direction of research on the way to quantum computing is to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics. We address some semiconductor approach based on spin orbit coupling in semiconductor nanostructures. (authors)

  13. Interpreting quantum coherence through a quantum measurement process

    Science.gov (United States)

    Yao, Yao; Dong, G. H.; Xiao, Xing; Li, Mo; Sun, C. P.

    2017-11-01

    Recently, there has been a renewed interest in the quantification of coherence or other coherencelike concepts within the framework of quantum resource theory. However, rigorously defined or not, the notion of coherence or decoherence has already been used by the community for decades since the advent of quantum theory. Intuitively, the definitions of coherence and decoherence should be two sides of the same coin. Therefore, a natural question is raised: How can the conventional decoherence processes, such as the von Neumann-Lüders (projective) measurement postulation or partially dephasing channels, fit into the bigger picture of the recently established theoretical framework? Here we show that the state collapse rules of the von Neumann or Lüders-type measurements, as special cases of genuinely incoherent operations (GIOs), are consistent with the resource theories of quantum coherence. New hierarchical measures of coherence are proposed for the Lüders-type measurement and their relationship with measurement-dependent discord is addressed. Moreover, utilizing the fixed-point theory for C* algebra, we prove that GIOs indeed represent a particular type of partially dephasing (phase-damping) channels which have a matrix representation based on the Schur product. By virtue of the Stinespring dilation theorem, the physical realizations of incoherent operations are investigated in detail and we find that GIOs in fact constitute the core of strictly incoherent operations and generally incoherent operations and the unspeakable notion of coherence induced by GIOs can be transferred to the theories of speakable coherence by the corresponding permutation or relabeling operators.

  14. Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Claudio Cremaschini

    2017-07-01

    Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

  15. Numerical and analytical solutions for problems relevant for quantum computers

    International Nuclear Information System (INIS)

    Spoerl, Andreas

    2008-01-01

    Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)

  16. Connections among quantum logics

    International Nuclear Information System (INIS)

    Lock, P.F.; Hardegree, G.M.

    1985-01-01

    In this paper, a theory of quantum logics is proposed which is general enough to enable us to reexamine a previous work on quantum logics in the context of this theory. It is then easy to assess the differences between the different systems studied. The quantum logical systems which are incorporated are divided into two groups which we call ''quantum propositional logics'' and ''quantum event logics''. The work of Kochen and Specker (partial Boolean algebras) is included and so is that of Greechie and Gudder (orthomodular partially ordered sets), Domotar (quantum mechanical systems), and Foulis and Randall (operational logics) in quantum propositional logics; and Abbott (semi-Boolean algebras) and Foulis and Randall (manuals) in quantum event logics, In this part of the paper, an axiom system for quantum propositional logics is developed and the above structures in the context of this system examined. (author)

  17. Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

    International Nuclear Information System (INIS)

    Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang

    2014-01-01

    In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same

  18. Role of memory errors in quantum repeaters

    International Nuclear Information System (INIS)

    Hartmann, L.; Kraus, B.; Briegel, H.-J.; Duer, W.

    2007-01-01

    We investigate the influence of memory errors in the quantum repeater scheme for long-range quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable waiting times for classical signals. We show how to overcome these limitations by (i) improving local memory and (ii) introducing two operational modes of the quantum repeater. In both operational modes, the repeater is run blindly, i.e., without waiting for classical signals to arrive. In the first scheme, entanglement purification protocols based on one-way classical communication are used allowing to communicate over arbitrary distances. However, the error thresholds for noise in local control operations are very stringent. The second scheme makes use of entanglement purification protocols with two-way classical communication and inherits the favorable error thresholds of the repeater run in standard mode. One can increase the possible communication distance by an order of magnitude with reasonable overhead in physical resources. We outline the architecture of a quantum repeater that can possibly ensure intercontinental quantum communication

  19. Asymptotic evolution of quantum Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

    2012-07-01

    The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.

  20. QUANTUM: A Wolfram Mathematica add-on for Dirac Bra-Ket Notation, Non-Commutative Algebra, and Simulation of Quantum Computing Circuits

    International Nuclear Information System (INIS)

    Muñoz, J L Gómez; Delgado, F

    2016-01-01

    This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics. (paper)

  1. Sufficient condition for a quantum state to be genuinely quantum non-Gaussian

    Science.gov (United States)

    Happ, L.; Efremov, M. A.; Nha, H.; Schleich, W. P.

    2018-02-01

    We show that the expectation value of the operator \\hat{{ \\mathcal O }}\\equiv \\exp (-c{\\hat{x}}2)+\\exp (-c{\\hat{p}}2) defined by the position and momentum operators \\hat{x} and \\hat{p} with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.

  2. Local quantum thermal susceptibility

    Science.gov (United States)

    de Pasquale, Antonella; Rossini, Davide; Fazio, Rosario; Giovannetti, Vittorio

    2016-09-01

    Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties originate from averaging procedures which smoothen out local details. While undoubtedly successful, elegant and formally correct, this approach carries over an operational problem, namely determining the precision at which such variables are inferred, when technical/practical limitations restrict our capabilities to local probing. Here we introduce the local quantum thermal susceptibility, a quantifier for the best achievable accuracy for temperature estimation via local measurements. Our method relies on basic concepts of quantum estimation theory, providing an operative strategy to address the local thermal response of arbitrary quantum systems at equilibrium. At low temperatures, it highlights the local distinguishability of the ground state from the excited sub-manifolds, thus providing a method to locate quantum phase transitions.

  3. Fluctuations in quantum devices

    Directory of Open Access Journals (Sweden)

    H.Haken

    2004-01-01

    Full Text Available Logical gates can be formalized by Boolean algebra whose elementary operations can be realized by devices that employ the interactions of macroscopic numbers of elementary excitations such as electrons, holes, photons etc. With increasing miniaturization to the nano scale and below, quantum fluctuations become important and can no longer be ignored. Based on Heisenberg equations of motion for the creation and annihilation operators of elementary excitations, I determine the noise sources of composite quantum systems.

  4. Simulation of quantum dynamics based on the quantum stochastic differential equation.

    Science.gov (United States)

    Li, Ming

    2013-01-01

    The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

  5. Graphene quantum interference photodetector

    Directory of Open Access Journals (Sweden)

    Mahbub Alam

    2015-03-01

    Full Text Available In this work, a graphene quantum interference (QI photodetector was simulated in two regimes of operation. The structure consists of a graphene nanoribbon, Mach–Zehnder interferometer (MZI, which exhibits a strongly resonant transmission of electrons of specific energies. In the first regime of operation (that of a linear photodetector, low intensity light couples two resonant energy levels, resulting in scattering and differential transmission of current with an external quantum efficiency of up to 5.2%. In the second regime of operation, full current switching is caused by the phase decoherence of the current due to a strong photon flux in one or both of the interferometer arms in the same MZI structure. Graphene QI photodetectors have several distinct advantages: they are of very small size, they do not require p- and n-doped regions, and they exhibit a high external quantum efficiency.

  6. Fraunhofer regime of operation for superconducting quantum interference filters

    DEFF Research Database (Denmark)

    Shadrin, A.V.; Constantinian, K.Y.; Ovsyannikov, G.A.

    2008-01-01

    Series arrays of superconducting quantum interference devices (SQUIDs) with incommensurate loop areas, so-called superconducting quantum interference filters (SQIFs), are investigated in the kilohertz and the gigahertz frequency range. In SQIFs made of high-T-c bicrystal junctions the flux...... range of more than 60 dB in the kilohertz range. In the 1-2 GHz range the estimated power gain is 20 dB and the magnetic flux noise level is as low as 10(-4)Phi(0)....

  7. Conditions for uniqueness of product representations for separable quantum channels and separable quantum states

    International Nuclear Information System (INIS)

    Cohen, Scott M.

    2014-01-01

    We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number of parties. This result has implications for efforts to determine whether or not a given separable channel can be exactly implemented by local operations and classical communication. By the Choi-Jamiolkowski isomorphism, it also translates to a condition for the uniqueness of product state ensembles representing a given quantum state. These ideas follow from considerations concerning whether or not a subspace spanned by a given set of product operators contains at least one additional product operator

  8. Silicon based quantum dot hybrid qubits

    Science.gov (United States)

    Kim, Dohun

    2015-03-01

    The charge and spin degrees of freedom of an electron constitute natural bases for constructing quantum two level systems, or qubits, in semiconductor quantum dots. The quantum dot charge qubit offers a simple architecture and high-speed operation, but generally suffers from fast dephasing due to strong coupling of the environment to the electron's charge. On the other hand, quantum dot spin qubits have demonstrated long coherence times, but their manipulation is often slower than desired for important future applications. This talk will present experimental progress of a `hybrid' qubit, formed by three electrons in a Si/SiGe double quantum dot, which combines desirable characteristics (speed and coherence) in the past found separately in qubits based on either charge or spin degrees of freedom. Using resonant microwaves, we first discuss qubit operations near the `sweet spot' for charge qubit operation. Along with fast (>GHz) manipulation rates for any rotation axis on the Bloch sphere, we implement two independent tomographic characterization schemes in the charge qubit regime: traditional quantum process tomography (QPT) and gate set tomography (GST). We also present resonant qubit operations of the hybrid qubit performed on the same device, DC pulsed gate operations of which were recently demonstrated. We demonstrate three-axis control and the implementation of dynamic decoupling pulse sequences. Performing QPT on the hybrid qubit, we show that AC gating yields π rotation process fidelities higher than 93% for X-axis and 96% for Z-axis rotations, which demonstrates efficient quantum control of semiconductor qubits using resonant microwaves. We discuss a path forward for achieving fidelities better than the threshold for quantum error correction using surface codes. This work was supported in part by ARO (W911NF-12-0607), NSF (PHY-1104660), DOE (DE-FG02-03ER46028), and by the Laboratory Directed Research and Development program at Sandia National Laboratories

  9. Towards a feasible implementation of quantum neural networks using quantum dots

    International Nuclear Information System (INIS)

    Altaisky, Mikhail V.; Zolnikova, Nadezhda N.; Kaputkina, Natalia E.; Krylov, Victor A.; Lozovik, Yurii E.; Dattani, Nikesh S.

    2016-01-01

    We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations, which are based on SQUID-based systems operating at temperatures in the mK range.

  10. Quantum computation over the butterfly network

    International Nuclear Information System (INIS)

    Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S.; Murao, Mio

    2011-01-01

    In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A 76, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.

  11. Engineering quantum dynamics

    International Nuclear Information System (INIS)

    Lloyd, Seth; Viola, Lorenza

    2002-01-01

    The ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control, allows one to control the system to follow any desired coherent or incoherent quantum dynamics. Such universal dynamical control can be achieved, in principle, through the repeated application of only two coherent control operations and a simple 'Yes-No' measurement. As a consequence, a quantum computer can simulate an arbitrary open-system dynamics using just one qubit more than required to simulate closed-system dynamics

  12. Physics: quantum mechanics

    International Nuclear Information System (INIS)

    Basdevant, J.L.

    1983-01-01

    From important experiment descriptions (sometimes, intentionally simplified), the essential concepts in Quantum Mechanics are first introduced. Wave function notion is described, Schroedinger equation is established, and, after applications rich in physical signification, quantum state and Hilbert space formalism are introduced, which will help to understand many essential phenomena. Then the quantum mechanic general formulation is written and some important consequences are deduced. This formalism is applied to a simple physical problem series (angular momentum, hydrogen atom, etc.) aiming at assimilating the theory operation and its application [fr

  13. Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models

    Energy Technology Data Exchange (ETDEWEB)

    Niccoli, G.

    2009-12-15

    In an earlier paper (G. Niccoli and J. Teschner, 2009), the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization. (orig.)

  14. Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models

    International Nuclear Information System (INIS)

    Niccoli, G.

    2009-12-01

    In an earlier paper (G. Niccoli and J. Teschner, 2009), the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization. (orig.)

  15. Projective measurements in quantum and classical optical systems

    CSIR Research Space (South Africa)

    Roux, FS

    2014-09-01

    Full Text Available equally well to both classical and quantum optical systems. A projective measurement, in the context of quantum mechanics, is understood to be the process where a projection operator operates on some input state. Often this projection operator is composed...) Projective measurements in quantum and classical optical systems Filippus S. Roux* and Yingwen Zhang CSIR National Laser Centre, P.O. Box 395, Pretoria 0001, South Africa (Received 3 July 2014; published 22 September 2014) Experimental setups for the optical...

  16. Geometry of quantum computation with qutrits.

    Science.gov (United States)

    Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming

    2013-01-01

    Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.

  17. Quantum double actions on operator algebras and orbifold quantum field theories

    International Nuclear Information System (INIS)

    Mueger, M.

    1996-06-01

    Starting from a local quantum field theory with an unbroken compact symmetry group G in 1+1 dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region. Enlarging the local algebras by these disorder fields we obtain a nonlocal field theory, the fixpoint algebras of which under the appropriately extended action of the group G are shown to satisfy Haag duality in every simple sector. The specifically 1+1 dimensional phenomenon of violation of Haag duality of fixpoint nets is thereby clarified. In the case of a finite group G the extended theory is acted upon in a completely canonical way by the quantum double D(G) and satisfies R-matrix commutation relations as well as a Verlinde algebra. Furthermore, our methods are suitable for a concise and transparent approach to bosonization. The main technical ingredient is a strengthened version of the split property which should hold in all reasonable massive theories. In the appendices (part of) the results are extended to arbitary locally compact groups and our methods are adapted to chiral theories on the circle. (orig.)

  18. Quantum deformation of the affine transformation algebra

    International Nuclear Information System (INIS)

    Aizawa, N.; Sato, Haru-Tada

    1994-01-01

    We discuss a quantum deformation of the affine transformation algebra in one-dimensional space. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. (orig.)

  19. Universal quantum computation in a semiconductor quantum wire network

    International Nuclear Information System (INIS)

    Sau, Jay D.; Das Sarma, S.; Tewari, Sumanta

    2010-01-01

    Universal quantum computation (UQC) using Majorana fermions on a two-dimensional topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include any two-qubit gate and also no single-qubit π/8 phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, etc.), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an s-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic-state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of 0.14 as compared to 10 -3 to 10 -4 in ordinary unprotected quantum computation.

  20. Universality of black hole quantum computing

    Energy Technology Data Exchange (ETDEWEB)

    Dvali, Gia [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany); New York Univ., NY (United States). Center for Cosmology and Particle Physics; Gomez, Cesar [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC; Luest, Dieter [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Max-Planck-Institut fuer Physik, Muenchen (Germany); Omar, Yasser [Instituto de Telecomunicacoes (Portugal). Physics of Information and Quantum Technologies Group; Lisboa Univ. (Portugal). Inst. Superior Tecnico; Richter, Benedikt [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Instituto de Telecomunicacoes (Portugal). Physics of Information and Quantum Technologies Group; Lisboa Univ. (Portugal). Inst. Superior Tecnico

    2017-01-15

    By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  1. Quantum Transduction with Adaptive Control

    Science.gov (United States)

    Zhang, Mengzhen; Zou, Chang-Ling; Jiang, Liang

    2018-01-01

    Quantum transducers play a crucial role in hybrid quantum networks. A good quantum transducer can faithfully convert quantum signals from one mode to another with minimum decoherence. Most investigations of quantum transduction are based on the protocol of direct mode conversion. However, the direct protocol requires the matching condition, which in practice is not always feasible. Here we propose an adaptive protocol for quantum transducers, which can convert quantum signals without requiring the matching condition. The adaptive protocol only consists of Gaussian operations, feasible in various physical platforms. Moreover, we show that the adaptive protocol can be robust against imperfections associated with finite squeezing, thermal noise, and homodyne detection, and it can be implemented to realize quantum state transfer between microwave and optical modes.

  2. Quantum Transduction with Adaptive Control.

    Science.gov (United States)

    Zhang, Mengzhen; Zou, Chang-Ling; Jiang, Liang

    2018-01-12

    Quantum transducers play a crucial role in hybrid quantum networks. A good quantum transducer can faithfully convert quantum signals from one mode to another with minimum decoherence. Most investigations of quantum transduction are based on the protocol of direct mode conversion. However, the direct protocol requires the matching condition, which in practice is not always feasible. Here we propose an adaptive protocol for quantum transducers, which can convert quantum signals without requiring the matching condition. The adaptive protocol only consists of Gaussian operations, feasible in various physical platforms. Moreover, we show that the adaptive protocol can be robust against imperfections associated with finite squeezing, thermal noise, and homodyne detection, and it can be implemented to realize quantum state transfer between microwave and optical modes.

  3. Bohrification of operator algebras and quantum logic

    NARCIS (Netherlands)

    Heunen, C.; Landsman, N.P.; Spitters, B.A.W.

    2012-01-01

    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by

  4. Bohrification of operator algebras and quantum logic

    NARCIS (Netherlands)

    Heunen, C.; Landsman, N.P.; Spitters, B.A.W.

    2009-01-01

    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by

  5. Actively Secure Two-Party Evaluation of Any Quantum Operation

    DEFF Research Database (Denmark)

    Dupuis, Frédéric; Nielsen, Jesper Buus; Salvail, Louis

    2012-01-01

    We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, trace-preserving map , given as a quantum circuit, upon their joint quantum input state . Our protocol leaks no more to any active adversary than an ideal ...... functionality for provided Alice and Bob have the cryptographic resources for active secure two-party classical computation. Our protocol is constructed from the protocol for the same task secure against specious adversaries presented in [4]....

  6. Quantum communication in noisy environments

    International Nuclear Information System (INIS)

    Aschauer, H.

    2004-01-01

    In this thesis, we investigate how protocols in quantum communication theory are influenced by noise. Specifically, we take into account noise during the transmission of quantum information and noise during the processing of quantum information. We describe three novel quantum communication protocols which can be accomplished efficiently in a noisy environment: (1) Factorization of Eve: We show that it is possible to disentangle transmitted qubits a posteriori from the quantum channel's degrees of freedom. (2) Cluster state purification: We give multi-partite entanglement purification protocols for a large class of entangled quantum states. (3) Entanglement purification protocols from quantum codes: We describe a constructive method to create bipartite entanglement purification protocols form quantum error correcting codes, and investigate the properties of these protocols, which can be operated in two different modes, which are related to quantum communication and quantum computation protocols, respectively

  7. About the velocity operator for spinning particles in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Salesi, Giovanni [Universita Statale di Catania (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Catania (Italy); Recami, Erasmo; Rodrigues Junior, Waldyr A. [Universidade Estadual de Campinas, SP (Brazil). Dept. de Matematica Aplicada

    1995-12-01

    Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into sensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector. (author). 19 refs.

  8. About the velocity operator for spinning particles in quantum mechanics

    International Nuclear Information System (INIS)

    Salesi, Giovanni; Recami, Erasmo; Rodrigues Junior, Waldyr A.

    1995-12-01

    Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into sensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector. (author). 19 refs

  9. The potential of the quantum computer

    CERN Multimedia

    2006-01-01

    The Physics Section of the University of Geneva is continuing its series of lectures, open to the general public, on the most recent developments in the field of physics. The next lecture, given by Professor Michel Devoret of Yale University in the United States, will be on the potential of the quantum computer. The quantum computer is, as yet, a hypothetical machine which would operate on the basic principles of quantum mechanics. Compared to standard computers, it represents a significant gain in computing power for certain complex calculations. Quantum operations can simultaneously explore a very large number of possibilities. The correction of quantum errors, which until recently had been deemed impossible, has now become a well-established technique. Several prototypes for, as yet, very simple quantum processors have been developed. The lecture will begin with a demonstration in the auditorium of the detection of cosmic rays and, in collaboration with Professor E. Ellberger of the Conservatoire de M...

  10. Expressing stochastic unravellings using random evolution operators

    International Nuclear Information System (INIS)

    Salgado, D; Sanchez-Gomez, J L

    2002-01-01

    We prove how the form of the most general invariant stochastic unravelling for Markovian (recently given in the literature by Wiseman and Diosi) and non-Markovian but Lindblad-type open quantum systems can be attained by imposing a single mathematical condition upon the random evolution operator of the system, namely a.s. trace preservation (a.s. stands for almost surely). The use of random operators ensures the complete positivity of the density operator evolution and characterizes the linear/non-linear character of the evolution in a straightforward way. It is also shown how three quantum stochastic evolution models - continuous spontaneous localization, quantum state diffusion and quantum mechanics with universal position localization - appear as concrete choices for the noise term of the evolution random operators are assumed. We finally conjecture how these operators may in the future be used in two different directions: both to connect quantum stochastic evolution models with random properties of space-time and to handle noisy quantum logical gates

  11. Quantum logic between remote quantum registers

    Science.gov (United States)

    Yao, N. Y.; Gong, Z.-X.; Laumann, C. R.; Bennett, S. D.; Duan, L.-M.; Lukin, M. D.; Jiang, L.; Gorshkov, A. V.

    2013-02-01

    We consider two approaches to dark-spin-mediated quantum computing in hybrid solid-state spin architectures. First, we review the notion of eigenmode-mediated unpolarized spin-chain state transfer and extend the analysis to various experimentally relevant imperfections: quenched disorder, dynamical decoherence, and uncompensated long-range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further briefly consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing that exploits all of the dark spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate dark-spin qubits significantly raise the error threshold for robust operation. Finally, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated nitrogen-vacancy registers in diamond; disorder-averaged numerics confirm that high-fidelity gates are achievable even in the presence of moderate disorder.

  12. Local quantum thermal susceptibility

    Science.gov (United States)

    De Pasquale, Antonella; Rossini, Davide; Fazio, Rosario; Giovannetti, Vittorio

    2016-01-01

    Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties originate from averaging procedures which smoothen out local details. While undoubtedly successful, elegant and formally correct, this approach carries over an operational problem, namely determining the precision at which such variables are inferred, when technical/practical limitations restrict our capabilities to local probing. Here we introduce the local quantum thermal susceptibility, a quantifier for the best achievable accuracy for temperature estimation via local measurements. Our method relies on basic concepts of quantum estimation theory, providing an operative strategy to address the local thermal response of arbitrary quantum systems at equilibrium. At low temperatures, it highlights the local distinguishability of the ground state from the excited sub-manifolds, thus providing a method to locate quantum phase transitions. PMID:27681458

  13. Quantum gravito-optics: a light route from semiclassical gravity to quantum gravity

    International Nuclear Information System (INIS)

    Unnikrishnan, C S; Gillies, George T

    2015-01-01

    Quantum gravity remains an elusive theory, in spite of our thorough understanding of the quantum theory and the general theory of relativity separately, presumably due to the lack of any observational clues. We argue that the theory of quantum gravity has a strong constraining anchor in the sector of gravitational radiation, ensuring reliable physical clues, albeit in a limited observable form. In particular, all types of gravitational waves expected to be observable in LIGO-like advanced detectors are fully quantum mechanical states of radiation. Exact equivalence of the full quantum gravity theory with the familiar semiclassical theory is ensured in the radiation sector, in most real situations where the relevant quantum operator functions are normal ordered, by the analogue of the optical equivalence theorem in quantum optics. We show that this is indeed the case for the detection of the waves from a massive binary system, a single gravitational atom, that emits coherent radiation. The idea of quantum-gravitational optics can assist in guiding along the fuzzy roads to quantum gravity. (paper)

  14. Quantum logic networks for probabilistic teleportation

    Institute of Scientific and Technical Information of China (English)

    刘金明; 张永生; 等

    2003-01-01

    By eans of the primitive operations consisting of single-qubit gates.two-qubit controlled-not gates,Von Neuman measurement and classically controlled operations.,we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit,a two-particle entangled state,and an N-particle entanglement.Based on the quantum networks,we show that after the partially entangled states are concentrated into maximal entanglement,the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.

  15. On the quantum inverse scattering problem

    International Nuclear Information System (INIS)

    Maillet, J.M.; Terras, V.

    2000-01-01

    A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains

  16. Holonomic surface codes for fault-tolerant quantum computation

    Science.gov (United States)

    Zhang, Jiang; Devitt, Simon J.; You, J. Q.; Nori, Franco

    2018-02-01

    Surface codes can protect quantum information stored in qubits from local errors as long as the per-operation error rate is below a certain threshold. Here we propose holonomic surface codes by harnessing the quantum holonomy of the system. In our scheme, the holonomic gates are built via auxiliary qubits rather than the auxiliary levels in multilevel systems used in conventional holonomic quantum computation. The key advantage of our approach is that the auxiliary qubits are in their ground state before and after each gate operation, so they are not involved in the operation cycles of surface codes. This provides an advantageous way to implement surface codes for fault-tolerant quantum computation.

  17. Quantum kinetic theory

    CERN Document Server

    Bonitz, Michael

    2016-01-01

    This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.

  18. Quantum Inequalities and Sequential Measurements

    International Nuclear Information System (INIS)

    Candelpergher, B.; Grandouz, T.; Rubinx, J.L.

    2011-01-01

    In this article, the peculiar context of sequential measurements is chosen in order to analyze the quantum specificity in the two most famous examples of Heisenberg and Bell inequalities: Results are found at some interesting variance with customary textbook materials, where the context of initial state re-initialization is described. A key-point of the analysis is the possibility of defining Joint Probability Distributions for sequential random variables associated to quantum operators. Within the sequential context, it is shown that Joint Probability Distributions can be defined in situations where not all of the quantum operators (corresponding to random variables) do commute two by two. (authors)

  19. Robust Learning Control Design for Quantum Unitary Transformations.

    Science.gov (United States)

    Wu, Chengzhi; Qi, Bo; Chen, Chunlin; Dong, Daoyi

    2017-12-01

    Robust control design for quantum unitary transformations has been recognized as a fundamental and challenging task in the development of quantum information processing due to unavoidable decoherence or operational errors in the experimental implementation of quantum operations. In this paper, we extend the systematic methodology of sampling-based learning control (SLC) approach with a gradient flow algorithm for the design of robust quantum unitary transformations. The SLC approach first uses a "training" process to find an optimal control strategy robust against certain ranges of uncertainties. Then a number of randomly selected samples are tested and the performance is evaluated according to their average fidelity. The approach is applied to three typical examples of robust quantum transformation problems including robust quantum transformations in a three-level quantum system, in a superconducting quantum circuit, and in a spin chain system. Numerical results demonstrate the effectiveness of the SLC approach and show its potential applications in various implementation of quantum unitary transformations.

  20. Hamiltonian theories quantization based on a probability operator

    International Nuclear Information System (INIS)

    Entral'go, E.E.

    1986-01-01

    The quantization method with a linear reflection of classical coordinate-momentum-time functions Λ(q,p,t) at quantum operators in a space of quantum states ψ, is considered. The probability operator satisfies a system of equations representing the principles of dynamical and canonical correspondences between the classical and quantum theories. The quantization based on a probability operator leads to a quantum theory with a nonnegative joint coordinate-momentum distribution function for any state ψ. The main consequences of quantum mechanics with a probability operator are discussed in comparison with the generally accepted quantum and classical theories. It is shown that a probability operator leads to an appearance of some new notions called ''subquantum'' ones. Hence the quantum theory with a probability operator does not pretend to any complete description of physical reality in terms of classical variables and by this reason contains no problems like Einstein-Podolsky-Rosen paradox. The results of some concrete problems are given: a free particle, a harmonic oscillator, an electron in the Coulomb field. These results give hope on the possibility of an experimental verification of the quantization based on a probability operator

  1. Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

    Science.gov (United States)

    Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

    2016-08-18

    Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

  2. Mathematical methods in physics distributions, Hilbert space operators, variational methods, and applications in quantum physics

    CERN Document Server

    Blanchard, Philippe

    2015-01-01

    The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas.  The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories.  All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods.   The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...

  3. On a new visualization tool for quantum systems and on a time-optimal control problem for quantum gates

    International Nuclear Information System (INIS)

    Garon, Ariane

    2014-01-01

    Since the foundations of quantum physics have been laid, our knowledge of it never ceased to grow and this field of science naturally split into diverse specialized branches. The first part of this thesis focuses on a problem which concerns all branches of quantum physics, which is the visualization of quantum systems. The non-intuitive aspect of quantum physics justifies a shared desire to visualize quantum systems. In the present work, we develop a method to visualize any operators in these systems, including in particular state operators (density matrices), Hamiltonians and propagators. The method, referred to as DROPS (Discrete Representation of spin OPeratorS), is based on a generalization of Wigner representations, presented in this document. The resulting visualization of an operator A is called its DROPS representation or visualization. We demonstrate its intuitive character by illustrating a series of concepts in nuclear magnetic resonance (NMR) spectroscopy for systems consisting of two spin-1/2 particles. The second part of this thesis is concerned with a problem of optimal control which finds applications in the fields of NMR spectroscopy, medical imagery and quantum computing, to cite a few. The problem of creating a propagator in the shortest amount of time is considered, and the results are extended to solve the closely related problem of creating rotations in the smallest amount of time. The approach used here differs from the previous results on the subject by solving the problem using the Pontryagin's maximum principle and by its detailed consideration of singular controls and trajectories.

  4. Primer of quantum mechanics

    CERN Document Server

    Chester, Marvin

    2003-01-01

    Introductory text examines the classical quantum bead on a track: its state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; and bead in a spherical shell. Also, spin, matrices and structure of quantum mechanics; simplest atom; indistinguishable particles; and stationary-state perturbation theory.

  5. Quantum Coherence, Time-Translation Symmetry, and Thermodynamics

    Directory of Open Access Journals (Sweden)

    Matteo Lostaglio

    2015-04-01

    Full Text Available The first law of thermodynamics imposes not just a constraint on the energy content of systems in extreme quantum regimes but also symmetry constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy. Moreover, the recently developed thermomajorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis.

  6. The foliation operator in history quantum field theory

    International Nuclear Information System (INIS)

    Isham, C.J.; Savvidou, K.

    2002-01-01

    As a preliminary to discussing the quantization of the foliation in a history form of general relativity, we show how the discussion in an earlier work [J. Math. Phys. 43, 3053 (2002)] of a history version of free, scalar quantum field theory can be augmented in such a way as to include the quantization of the unit-length, timelike vector that determines a Lorentzian foliation of Minkowski space-time. We employ a Hilbert bundle construction that is motivated by (i) discussing the role of the external Lorentz group in the existing history quantum field theory [J. Math. Phys. 43, 3053 (2002)] and (ii) considering a specific representation of the extended history algebra obtained from the multi-symplectic representation of scalar field theory

  7. Quantum information

    International Nuclear Information System (INIS)

    Rodgers, P.

    1998-01-01

    There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)

  8. Quantum information

    Energy Technology Data Exchange (ETDEWEB)

    Rodgers, P

    1998-03-01

    There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)

  9. Quantum Lie theory a multilinear approach

    CERN Document Server

    Kharchenko, Vladislav

    2015-01-01

    This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin  Lie algebras;  and Shestakov--Umirbaev  operations for the Lie theory of nonassociative products.  Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.

  10. Quantum Watermarking Scheme Based on INEQR

    Science.gov (United States)

    Zhou, Ri-Gui; Zhou, Yang; Zhu, Changming; Wei, Lai; Zhang, Xiafen; Ian, Hou

    2018-04-01

    Quantum watermarking technology protects copyright by embedding invisible quantum signal in quantum multimedia data. In this paper, a watermarking scheme based on INEQR was presented. Firstly, the watermark image is extended to achieve the requirement of embedding carrier image. Secondly, the swap and XOR operation is used on the processed pixels. Since there is only one bit per pixel, XOR operation can achieve the effect of simple encryption. Thirdly, both the watermark image extraction and embedding operations are described, where the key image, swap operation and LSB algorithm are used. When the embedding is made, the binary image key is changed. It means that the watermark has been embedded. Of course, if the watermark image is extracted, the key's state need detected. When key's state is |1>, this extraction operation is carried out. Finally, for validation of the proposed scheme, both the Signal-to-noise ratio (PSNR) and the security of the scheme are analyzed.

  11. CubeSat quantum communications mission

    Energy Technology Data Exchange (ETDEWEB)

    Oi, Daniel K.L. [University of Strathclyde, SUPA Department of Physics, Glasgow (United Kingdom); University of Strathclyde, Strathclyde Space Institute, Glasgow (United Kingdom); Ling, Alex [National University of Singapore, Centre for Quantum Technologies, Singapore (Singapore); National University of Singapore, Dept. of Physics, Singapore (Singapore); Vallone, Giuseppe; Villoresi, Paolo [Universita degli Studi di Padova, Dipartimento di Ingegneria dell' Informazione, Padova (Italy); Greenland, Steve; Kerr, Emma [University of Strathclyde, Advanced Space Concepts Laboratory, Mechanical and Aerospace Engineering, Glasgow (United Kingdom); Macdonald, Malcolm [Technology and Innovation Centre, Scottish Centre of Excellence in Satellite Applications, Glasgow (United Kingdom); Weinfurter, Harald [Ludwig-Maximilians-Universitaet, Department fuer Physik, Munich (Germany); Kuiper, Hans [Delft University of Technology, Space Systems Engineering, Aerospace Engineering, Delft (Netherlands); Charbon, Edoardo [AQUA, EPFL, Lausanne (Switzerland); Delft University of Technology, Delft (Netherlands); Ursin, Rupert [Vienna Austrian Academy of Sciences, Institute for Quantum Optics and Quantum Information, Vienna (Austria)

    2017-12-15

    Quantum communication is a prime space technology application and offers near-term possibilities for long-distance quantum key distribution (QKD) and experimental tests of quantum entanglement. However, there exists considerable developmental risks and subsequent costs and time required to raise the technological readiness level of terrestrial quantum technologies and to adapt them for space operations. The small-space revolution is a promising route by which synergistic advances in miniaturization of both satellite systems and quantum technologies can be combined to leap-frog conventional space systems development. Here, we outline a recent proposal to perform orbit-to-ground transmission of entanglement and QKD using a CubeSat platform deployed from the International Space Station (ISS). This ambitious mission exploits advances in nanosatellite attitude determination and control systems (ADCS), miniaturised target acquisition and tracking sensors, compact and robust sources of single and entangled photons, and high-speed classical communications systems, all to be incorporated within a 10 kg 6 litre mass-volume envelope. The CubeSat Quantum Communications Mission (CQuCoM) would be a pathfinder for advanced nanosatellite payloads and operations, and would establish the basis for a constellation of low-Earth orbit trusted-nodes for QKD service provision. (orig.)

  12. CubeSat quantum communications mission

    International Nuclear Information System (INIS)

    Oi, Daniel K.L.; Ling, Alex; Vallone, Giuseppe; Villoresi, Paolo; Greenland, Steve; Kerr, Emma; Macdonald, Malcolm; Weinfurter, Harald; Kuiper, Hans; Charbon, Edoardo; Ursin, Rupert

    2017-01-01

    Quantum communication is a prime space technology application and offers near-term possibilities for long-distance quantum key distribution (QKD) and experimental tests of quantum entanglement. However, there exists considerable developmental risks and subsequent costs and time required to raise the technological readiness level of terrestrial quantum technologies and to adapt them for space operations. The small-space revolution is a promising route by which synergistic advances in miniaturization of both satellite systems and quantum technologies can be combined to leap-frog conventional space systems development. Here, we outline a recent proposal to perform orbit-to-ground transmission of entanglement and QKD using a CubeSat platform deployed from the International Space Station (ISS). This ambitious mission exploits advances in nanosatellite attitude determination and control systems (ADCS), miniaturised target acquisition and tracking sensors, compact and robust sources of single and entangled photons, and high-speed classical communications systems, all to be incorporated within a 10 kg 6 litre mass-volume envelope. The CubeSat Quantum Communications Mission (CQuCoM) would be a pathfinder for advanced nanosatellite payloads and operations, and would establish the basis for a constellation of low-Earth orbit trusted-nodes for QKD service provision. (orig.)

  13. Model of a programmable quantum processing unit based on a quantum transistor effect

    Science.gov (United States)

    Ablayev, Farid; Andrianov, Sergey; Fetisov, Danila; Moiseev, Sergey; Terentyev, Alexandr; Urmanchev, Andrey; Vasiliev, Alexander

    2018-02-01

    In this paper we propose a model of a programmable quantum processing device realizable with existing nano-photonic technologies. It can be viewed as a basis for new high performance hardware architectures. Protocols for physical implementation of device on the controlled photon transfer and atomic transitions are presented. These protocols are designed for executing basic single-qubit and multi-qubit gates forming a universal set. We analyze the possible operation of this quantum computer scheme. Then we formalize the physical architecture by a mathematical model of a Quantum Processing Unit (QPU), which we use as a basis for the Quantum Programming Framework. This framework makes it possible to perform universal quantum computations in a multitasking environment.

  14. Quantum Secure Group Communication.

    Science.gov (United States)

    Li, Zheng-Hong; Zubairy, M Suhail; Al-Amri, M

    2018-03-01

    We propose a quantum secure group communication protocol for the purpose of sharing the same message among multiple authorized users. Our protocol can remove the need for key management that is needed for the quantum network built on quantum key distribution. Comparing with the secure quantum network based on BB84, we show our protocol is more efficient and securer. Particularly, in the security analysis, we introduce a new way of attack, i.e., the counterfactual quantum attack, which can steal information by "invisible" photons. This invisible photon can reveal a single-photon detector in the photon path without triggering the detector. Moreover, the photon can identify phase operations applied to itself, thereby stealing information. To defeat this counterfactual quantum attack, we propose a quantum multi-user authorization system. It allows us to precisely control the communication time so that the attack can not be completed in time.

  15. Continuous-Wave Operation of GaN Based Multi-Quantum-Well Laser Diode at Room Temperature

    International Nuclear Information System (INIS)

    Li-Qun, Zhang; Shu-Ming, Zhang; Hui, Yang; Lian, Ji; Jian-Jun, Zhu; Zong-Shun, Liu; De-Gang, Zhao; De-Sheng, Jiang; Li-Hong, Duan; Hai, Wang; Yong-Sheng, Shi; Su-Ying, Liu; Jun-Wu, Liang; Qing, Cao; Liang-Hui, Chen

    2008-01-01

    Room-temperature operation of cw GaN based multi-quantum-well laser diodes (LDs) is demonstrated. The LD structure is grown on a sapphire (0001) substrate by metalorganic chemical vapour deposition. A 2.5μm × 800μm ridge waveguide structure is fabricated. The electrical and optical characteristics of the laser diode under direct current injection at room temperature are investigated. The threshold current and voltage of the LD under cw operation are 110 mA and 10.5 V, respectively. Thermal induced series resistance decrease and emission wavelength red-shift are observed as the injection current is increased. The full width at half maximum for the parallel and perpendicular far field pattern (FFP) are 12° and 32°, respectively

  16. Concatenated codes for fault tolerant quantum computing

    Energy Technology Data Exchange (ETDEWEB)

    Knill, E.; Laflamme, R.; Zurek, W.

    1995-05-01

    The application of concatenated codes to fault tolerant quantum computing is discussed. We have previously shown that for quantum memories and quantum communication, a state can be transmitted with error {epsilon} provided each gate has error at most c{epsilon}. We show how this can be used with Shor`s fault tolerant operations to reduce the accuracy requirements when maintaining states not currently participating in the computation. Viewing Shor`s fault tolerant operations as a method for reducing the error of operations, we give a concatenated implementation which promises to propagate the reduction hierarchically. This has the potential of reducing the accuracy requirements in long computations.

  17. Construction of a universal quantum computer

    International Nuclear Information System (INIS)

    Lagana, Antonio A.; Lohe, M. A.; Smekal, Lorenz von

    2009-01-01

    We construct a universal quantum computer following Deutsch's original proposal of a universal quantum Turing machine (UQTM). Like Deutsch's UQTM, our machine can emulate any classical Turing machine and can execute any algorithm that can be implemented in the quantum gate array framework but under the control of a quantum program, and hence is universal. We present the architecture of the machine, which consists of a memory tape and a processor and describe the observables that comprise the registers of the processor and the instruction set, which includes a set of operations that can approximate any unitary operation to any desired accuracy and hence is quantum computationally universal. We present the unitary evolution operators that act on the machine to achieve universal computation and discuss each of them in detail and specify and discuss explicit program halting and concatenation schemes. We define and describe a set of primitive programs in order to demonstrate the universal nature of the machine. These primitive programs facilitate the implementation of more complex algorithms and we demonstrate their use by presenting a program that computes the NAND function, thereby also showing that the machine can compute any classically computable function.

  18. Collapsing a perfect superposition to a chosen quantum state without measurement.

    Directory of Open Access Journals (Sweden)

    Ahmed Younes

    Full Text Available Given a perfect superposition of [Formula: see text] states on a quantum system of [Formula: see text] qubits. We propose a fast quantum algorithm for collapsing the perfect superposition to a chosen quantum state [Formula: see text] without applying any measurements. The basic idea is to use a phase destruction mechanism. Two operators are used, the first operator applies a phase shift and a temporary entanglement to mark [Formula: see text] in the superposition, and the second operator applies selective phase shifts on the states in the superposition according to their Hamming distance with [Formula: see text]. The generated state can be used as an excellent input state for testing quantum memories and linear optics quantum computers. We make no assumptions about the used operators and applied quantum gates, but our result implies that for this purpose the number of qubits in the quantum register offers no advantage, in principle, over the obvious measurement-based feedback protocol.

  19. Realization of quantum state privacy amplification in a nuclear magnetic resonance quantum system

    International Nuclear Information System (INIS)

    Hao, Liang; Wang, Chuan; Long, Gui Lu

    2010-01-01

    Quantum state privacy amplification (QSPA) is the quantum analogue of classical privacy amplification. If the state information of a series of single-particle states has some leakage, QSPA reduces this leakage by condensing the state information of two particles into the state of one particle. Recursive applications of the operations will eliminate the quantum state information leakage to a required minimum level. In this paper, we report the experimental implementation of a quantum state privacy amplification protocol in a nuclear magnetic resonance system. The density matrices of the states are constructed in the experiment, and the experimental results agree well with theory.

  20. Nonexistence of a universal quantum machine to examine the precision of unknown quantum states

    International Nuclear Information System (INIS)

    Pang, Shengshi; Wu, Shengjun; Chen, Zeng-Bing

    2011-01-01

    In this work, we reveal a type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any nontrivial threshold in a perfect or unambiguous way. This impossibility is distinct from the existing impossibilities in that it is a ''collective'' impossibility on multiple quantum states; most other ''no-go'' theorems are concerned with only one single state each time, i.e., it is an impossibility on a nonlocal quantum operation. This impossibility may provide new insight into the nature of quantum mechanics, and it implies more limitations on quantum information tasks than the existing no-go theorems.

  1. Dynamics of quantum discord in a quantum critical environment

    International Nuclear Information System (INIS)

    Xi Zhengjun; Li Yongming; Lu Xiaoming; Sun Zhe

    2011-01-01

    We study the dynamics of quantum discord (QD) of two qubits independently coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. For this model, we drive the corresponding Kraus operators, obtain the analytic results of QD and compare the dynamics of QD with the dynamics of relative entropy of entanglement nearby the critical point. It is shown that the impact of the quantum criticality environment on QD can be concentrated in a very narrow region nearby the critical point, so it supplies an efficient way to detect the critical points. In the vicinity of the critical point, the evolution of QD is shown to be more complicated than that of entanglement. Furthermore, we find that separable states can also be used to reflect the quantum criticality of the environment.

  2. Quantumness and the role of locality on quantum correlations

    Science.gov (United States)

    Bellomo, G.; Plastino, A.; Plastino, A. R.

    2016-06-01

    Quantum correlations in a physical system are usually studied with respect to a unique and fixed decomposition of the system into subsystems, without fully exploiting the rich structure of the state space. Here, we show several examples in which the consideration of different ways to decompose a physical system enhances the quantum resources and accounts for a more flexible definition of quantumness measures. Furthermore, we give a different perspective regarding how to reassess the fact that local operations play a key role in general quantumness measures that go beyond entanglement—as discordlike ones. We propose a family of measures to quantify the maximum quantumness of a given state. For the discord-based case, we present some analytical results for 2 ×d -dimensional states. Applying our definition to low-dimensional bipartite states, we show that different behaviors can be reported for separable and entangled states vis-à-vis those corresponding to the usual measures of quantum correlations. We show that there is a close link between our proposal and the criterion to witness quantum correlations based on the rank of the correlation matrix, proposed by Dakić, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010), 10.1103/PhysRevLett.105.190502].

  3. Quantum dressing orbits on compact groups

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B. (Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Sommerfeld Inst.); Stovicek, P. (Prague Univ. (Czechoslovakia). Dept. of Mathematics)

    1993-02-01

    The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.).

  4. Quantum dressing orbits on compact groups

    International Nuclear Information System (INIS)

    Jurco, B.; Stovicek, P.

    1993-01-01

    The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.)

  5. How to Build a Quantum Computer

    Science.gov (United States)

    Sanders, Barry C.

    2017-11-01

    Quantum computer technology is progressing rapidly with dozens of qubits and hundreds of quantum logic gates now possible. Although current quantum computer technology is distant from being able to solve computational problems beyond the reach of non-quantum computers, experiments have progressed well beyond simply demonstrating the requisite components. We can now operate small quantum logic processors with connected networks of qubits and quantum logic gates, which is a great stride towards functioning quantum computers. This book aims to be accessible to a broad audience with basic knowledge of computers, electronics and physics. The goal is to convey key notions relevant to building quantum computers and to present state-of-the-art quantum-computer research in various media such as trapped ions, superconducting circuits, photonics and beyond.

  6. Quasi quantum group covariant q-oscillators

    International Nuclear Information System (INIS)

    Schomerus, V.

    1992-05-01

    If q is a p-th root of unity there exists a quasi-co-associative truncated quantum group algebra U T q (sl 2 ) whose indecomposable representations are the physical representations of U q (sl 2 ), whose co-product yields the truneated tensor product of physical representations of U q (sl 2 ), and whose R-matrix satisfies quasi Yang Baxter equations. For primitive p-th roots q, we consider a 2-dimensional q-oscillator which admits U T q (sl 2 ) as a symmetry algebra. Its wave functions lie in a space F T q of 'functions on the truncated quantum plane', i.e. of polynomials in noncommuting complex coordinate functions z a , on which multiplication operators Z a and the elements of U T q (sl 2 ) can act. This illustrates the concept of quasi quantum planes. Due to the truncation, the Hilbert space of states is finite dimensional. The subspaces F T(n) of monomials in x a of n-th degree vanish for n ≥ p-1, and F T(n) carries the 2J+1 dimensional irreducible representation of U T q (sl 2 ) if n=2J, J=0, 1/2, ... 1/2(p-2). Partial derivatives δ a are introduced. We find a *-operation on the algebra of multiplication operators Z i and derivatives δ b such that the adjoints Z * a act as differentiation on the truncated quantum plane. Multiplication operators Z a ('creation operators') and their adjoints ('annihilation operators') obey q -1/2 -commutation relations. The *-operation is used to determine a positive definite scalar product on the truncated quantum plane F T q . Some natural candidates of Hamiltonians for the q-oscillators are determined. (orig./HSI)

  7. Layered Architecture for Quantum Computing

    Directory of Open Access Journals (Sweden)

    N. Cody Jones

    2012-07-01

    Full Text Available We develop a layered quantum-computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface-code quantum error correction. In doing so, we propose a new quantum-computer architecture based on optical control of quantum dots. The time scales of physical-hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum-dot architecture we study could solve such problems on the time scale of days.

  8. Eigenfunction method and mass operator in the quantum electrodynamics of a constant field

    International Nuclear Information System (INIS)

    Ritus, V.I.

    1978-01-01

    A method is presented for the calculation of radiative effects in the quantum electrodynamics of an intense constant field. It is based on the application of the mass operator eigenfunctions and on diagonalization of the operator. A compact expression for the proper value of the electron mass operator in an arbitrary constant field and the corresponding elastic scattering amplitude are found. The imaginary part of the amplitude determines the decay rate of various states of the electron in the field; the real part contains the mass shift and the anomalous magnetic and electric moments as functions of the field and electron momentum. THe anomalous electric moment which arises in a field with a pseudoscalar EH not equal to 0 and the anomalous magnetic moment in an electric field which tends to the double Schwinger value with increase of the field strength are found and investigated in detail as are the mass shift and decay rate of the ground state of an electron in an electric field. In a weak field the mass shift contains the linear with respect to the field modulus classical term which characterizes the effect of acceleration on the structure of electron

  9. Stochastic methods in quantum mechanics

    CERN Document Server

    Gudder, Stanley P

    2005-01-01

    Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun

  10. Scheme of thinking quantum systems

    International Nuclear Information System (INIS)

    Yukalov, V I; Sornette, D

    2009-01-01

    A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field

  11. Quantum simulation from the bottom up: the case of rebits

    Science.gov (United States)

    Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

    2018-05-01

    Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

  12. Quantacell: powerful charging of quantum batteries

    International Nuclear Information System (INIS)

    Binder, Felix C; Vinjanampathy, Sai; Modi, Kavan; Goold, John

    2015-01-01

    We study the problem of charging a quantum battery in finite time. We demonstrate an analytical optimal protocol for the case of a single qubit. Extending this analysis to an array of N qubits, we demonstrate that an N-fold advantage in power per qubit can be achieved when global operations are permitted. The exemplary analytic argument for this quantum advantage in the charging power is backed up by numerical analysis using optimal control techniques. It is demonstrated that the quantum advantage for power holds when, with cyclic operation in mind, initial and final states are required to be separable. (paper)

  13. A limit of the quantum Rényi divergence

    International Nuclear Information System (INIS)

    Datta, Nilanjana; Leditzky, Felix

    2014-01-01

    Recently, an interesting quantity called the quantum Rényi divergence (or ‘sandwiched’ Rényi relative entropy) was defined for pairs of positive semi-definite operators ρ and σ. It depends on a parameter α and acts as a parent quantity for other relative entropies which have important operational significance in quantum information theory: the quantum relative entropy and the min- and max-relative entropies. There is, however, another relative entropy, called the 0-relative Rényi entropy, which plays a key role in the analysis of various quantum information-processing tasks in the one-shot setting. We prove that the 0-relative Rényi entropy is obtainable from the quantum Rényi divergence only if ρ and σ have equal supports. This, along with existing results in the literature, suggests that it suffices to consider two essential parent quantities from which operationally relevant entropic quantities can be derived—the quantum Rényi divergence with parameter α ⩾ 1/2, and the α-relative Rényi entropy with α ∈ [0, 1). (paper)

  14. Quantum Discord Determines the Interferometric Power of Quantum States

    Science.gov (United States)

    Girolami, Davide; Souza, Alexandre M.; Giovannetti, Vittorio; Tufarelli, Tommaso; Filgueiras, Jefferson G.; Sarthour, Roberto S.; Soares-Pinto, Diogo O.; Oliveira, Ivan S.; Adesso, Gerardo

    2014-05-01

    Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually tailored to the particular dynamics whose parameters are being estimated. Here we consider a novel framework where quantum estimation is performed in an interferometric configuration, using bipartite probe states prepared when only the spectrum of the generating Hamiltonian is known. We introduce a figure of merit for the scheme, given by the worst-case precision over all suitable Hamiltonians, and prove that it amounts exactly to a computable measure of discord-type quantum correlations for the input probe. We complement our theoretical results with a metrology experiment, realized in a highly controllable room-temperature nuclear magnetic resonance setup, which provides a proof-of-concept demonstration for the usefulness of discord in sensing applications. Discordant probes are shown to guarantee a nonzero phase sensitivity for all the chosen generating Hamiltonians, while classically correlated probes are unable to accomplish the estimation in a worst-case setting. This work establishes a rigorous and direct operational interpretation for general quantum correlations, shedding light on their potential for quantum technology.

  15. Efficient networks for quantum factoring

    International Nuclear Information System (INIS)

    Beckman, D.; Chari, A.N.; Devabhaktuni, S.; Preskill, J.

    1996-01-01

    We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A K-bit number can be factored in time of order K 3 using a machine capable of storing 5K+1 qubits. Evaluation of the modular exponential function (the bottleneck of Shor close-quote s algorithm) could be achieved with about 72K 3 elementary quantum gates; implementation using a linear ion trap would require about 396K 3 laser pulses. A proof-of-principle demonstration of quantum factoring (factorization of 15) could be performed with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be a useful computer, it will be a powerful device for exploring experimentally the properties of entangled quantum states. copyright 1996 The American Physical Society

  16. A quantum extended Kalman filter

    International Nuclear Information System (INIS)

    Emzir, Muhammad F; Woolley, Matthew J; Petersen, Ian R

    2017-01-01

    In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements. (paper)

  17. A quantum extended Kalman filter

    Science.gov (United States)

    Emzir, Muhammad F.; Woolley, Matthew J.; Petersen, Ian R.

    2017-06-01

    In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.

  18. Quantum mechanics theory and experiment

    CERN Document Server

    Beck, Mark

    2012-01-01

    This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...

  19. Ultrafast quantum random number generation based on quantum phase fluctuations.

    Science.gov (United States)

    Xu, Feihu; Qi, Bing; Ma, Xiongfeng; Xu, He; Zheng, Haoxuan; Lo, Hoi-Kwong

    2012-05-21

    A quantum random number generator (QRNG) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics. Most approaches to QRNG employ single-photon detection technologies and are limited in speed. Here, we experimentally demonstrate an ultrafast QRNG at a rate over 6 Gbits/s based on the quantum phase fluctuations of a laser operating near threshold. Moreover, we consider a potential adversary who has partial knowledge on the raw data and discuss how one can rigorously remove such partial knowledge with postprocessing. We quantify the quantum randomness through min-entropy by modeling our system and employ two randomness extractors--Trevisan's extractor and Toeplitz-hashing--to distill the randomness, which is information-theoretically provable. The simplicity and high-speed of our experimental setup show the feasibility of a robust, low-cost, high-speed QRNG.

  20. Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

    Science.gov (United States)

    Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min

    1990-12-01

    Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

  1. Passive mode-locking dynamics in a 3.1GHz quantum dot laser diode operating around 1.5μm

    NARCIS (Netherlands)

    Tahvili, M.S.; Heck, M.J.R.; Nötzel, R.; Smit, M.K.; Bente, E.A.J.M.

    2010-01-01

    We report on passive mode-locking in a 3.1GHz InAs/InP(100) quantum dot laser diode operating around 1.5µm. The range of stable passive mode-locking, detailed measurements of the linewidth of the optical modes and the phase modulation in output pulses are presented.

  2. Quantum independent increment processes

    CERN Document Server

    Franz, Uwe

    2006-01-01

    This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.

  3. Optimal control of universal quantum gates in a double quantum dot

    Science.gov (United States)

    Castelano, Leonardo K.; de Lima, Emanuel F.; Madureira, Justino R.; Degani, Marcos H.; Maialle, Marcelo Z.

    2018-06-01

    We theoretically investigate electron spin operations driven by applied electric fields in a semiconductor double quantum dot (DQD) formed in a nanowire with longitudinal potential modulated by local gating. We develop a model that describes the process of loading and unloading the DQD taking into account the overlap between the electron wave function and the leads. Such a model considers the spatial occupation and the spin Pauli blockade in a time-dependent fashion due to the highly mixed states driven by the external electric field. Moreover, we present a road map based on the quantum optimal control theory (QOCT) to find a specific electric field that performs two-qubit quantum gates on a faster timescale and with higher possible fidelity. By employing the QOCT, we demonstrate the possibility of performing within high efficiency a universal set of quantum gates {cnot, H, and T } , where cnot is the controlled-not gate, H is the Hadamard gate, and T is the π /8 gate, even in the presence of the loading/unloading process and charge noise effects. Furthermore, by varying the intensity of the applied magnetic field B , the optimized fidelity of the gates oscillates with a period inversely proportional to the gate operation time tf. This behavior can be useful to attain higher fidelity for fast gate operations (>1 GHz) by appropriately choosing B and tf to produce a maximum of the oscillation.

  4. A mathematical companion to quantum mechanics

    CERN Document Server

    Sternberg, Shlomo

    2019-01-01

    This original 2018 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Topics include the Fourier transform, the spectral theorem for bounded self-joint operators, unbounded operators and semigroups, Weyl's theorem, the Rayleigh-Ritz method, one dimensional quantum mechanics, Ruelle's theorem, scattering theory, and many other subjects.

  5. Toy Models of a Nonassociative Quantum Mechanics

    International Nuclear Information System (INIS)

    Dzhunushaliev, V.

    2007-01-01

    Toy models of a nonassociative quantum mechanics are presented. The Heisenberg equation of motion is modified using a nonassociative commutator. Possible physical applications of a nonassociative quantum mechanics are considered. The idea is discussed that a nonassociative algebra could be the operator language for the nonperturbative quantum theory. In such approach the nonperturbative quantum theory has observables and un observables quantities.

  6. A surface code quantum computer in silicon

    Science.gov (United States)

    Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.

    2015-01-01

    The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310

  7. A surface code quantum computer in silicon.

    Science.gov (United States)

    Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L

    2015-10-01

    The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

  8. Quantum theory with an energy operator defined as a quartic form of the momentum

    Energy Technology Data Exchange (ETDEWEB)

    Bezák, Viktor, E-mail: bezak@fmph.uniba.sk

    2016-09-15

    Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke–Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined by the Yurke–Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.

  9. Quantum variational calculus

    CERN Document Server

    Malinowska, Agnieszka B

    2014-01-01

    This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...

  10. Speed limits for quantum gates in multiqubit systems

    NARCIS (Netherlands)

    Ashhab, S.; De Groot, P.C.; Nori, F.

    2012-01-01

    We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of

  11. Quantum algebra of N superspace

    International Nuclear Information System (INIS)

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-01-01

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the κ-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra

  12. Tunable single and dual mode operation of an external cavity quantum-dot injection laser

    International Nuclear Information System (INIS)

    Biebersdorf, A; Lingk, C; De Giorgi, M; Feldmann, J; Sacher, J; Arzberger, M; Ulbrich, C; Boehm, G; Amann, M-C; Abstreiter, G

    2003-01-01

    We investigate quantum-dot (QD) lasers in an external cavity using Littrow and Littman configurations. Here, we report on a continuously tunable QD laser with a broad tuning range from 1047 to 1130 nm with high stability and efficient side mode suppression. The full-width at half-maximum of the laser line is 0.85 nm determined mainly by the quality of the external grating. This laser can be operated in a dual-mode modus, where the mode-spacing can be tuned continuously between 1.1 and 34 nm. Simultaneous emission of the two laser modes is shown by sum frequency generation experiments

  13. Quantum information

    Energy Technology Data Exchange (ETDEWEB)

    Rodgers, P

    1998-03-01

    There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)

  14. Coherent states in quantum mechanics

    CERN Document Server

    Rodrigues, R D L; Fernandes, D

    2001-01-01

    We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.

  15. Autonomous calibration of single spin qubit operations

    Science.gov (United States)

    Frank, Florian; Unden, Thomas; Zoller, Jonathan; Said, Ressa S.; Calarco, Tommaso; Montangero, Simone; Naydenov, Boris; Jelezko, Fedor

    2017-12-01

    Fully autonomous precise control of qubits is crucial for quantum information processing, quantum communication, and quantum sensing applications. It requires minimal human intervention on the ability to model, to predict, and to anticipate the quantum dynamics, as well as to precisely control and calibrate single qubit operations. Here, we demonstrate single qubit autonomous calibrations via closed-loop optimisations of electron spin quantum operations in diamond. The operations are examined by quantum state and process tomographic measurements at room temperature, and their performances against systematic errors are iteratively rectified by an optimal pulse engineering algorithm. We achieve an autonomous calibrated fidelity up to 1.00 on a time scale of minutes for a spin population inversion and up to 0.98 on a time scale of hours for a single qubit π/2 -rotation within the experimental error of 2%. These results manifest a full potential for versatile quantum technologies.

  16. Arbitrated Quantum Signature with Hamiltonian Algorithm Based on Blind Quantum Computation

    Science.gov (United States)

    Shi, Ronghua; Ding, Wanting; Shi, Jinjing

    2018-03-01

    A novel arbitrated quantum signature (AQS) scheme is proposed motivated by the Hamiltonian algorithm (HA) and blind quantum computation (BQC). The generation and verification of signature algorithm is designed based on HA, which enables the scheme to rely less on computational complexity. It is unnecessary to recover original messages when verifying signatures since the blind quantum computation is applied, which can improve the simplicity and operability of our scheme. It is proved that the scheme can be deployed securely, and the extended AQS has some extensive applications in E-payment system, E-government, E-business, etc.

  17. Universal Quantum Computing with Arbitrary Continuous-Variable Encoding.

    Science.gov (United States)

    Lau, Hoi-Kwan; Plenio, Martin B

    2016-09-02

    Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.

  18. Entanglement production in quantum decision making

    International Nuclear Information System (INIS)

    Yukalov, V. I.; Sornette, D.

    2010-01-01

    The quantum decision theory introduced recently is formulated as a quantum theory of measurement. It describes prospect states represented by complex vectors of a Hilbert space over a prospect lattice. The prospect operators, acting in this space, form an involutive bijective algebra. A measure is defined for quantifying the entanglement produced by the action of prospect operators. This measure characterizes the level of complexity of prospects involved in decision making. An explicit expression is found for the maximal entanglement produced by the operators of multimode prospects.

  19. Proposal for a transmon-based quantum router

    NARCIS (Netherlands)

    Sala, Arnau; Blaauboer, M.

    2016-01-01

    We propose an implementation of a quantum router for microwave photons in a superconducting qubit architecture consisting of a transmon qubit, SQUIDs and a nonlinear capacitor. We model and analyze the dynamics of operation of the quantum switch using quantum Langevin equations in a scattering

  20. Quasi Hopf quantum symmetry in quantum theory

    International Nuclear Information System (INIS)

    Mack, G.; Schomerus, V.

    1991-05-01

    In quantum theory, internal symmetries more general than groups are possible. We show that quasitriangular quasi Hopf algebras G * as introduced by Drinfeld permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators as proposed by Froehlich. All this remains true when Drinfelds axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasitriangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G * admits a * -operation with certain properties. Invariance properties of Greens functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like U q (sl 2 ) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasitriangular quasi Hopf algebra G * is canonically associated with U q (sl 2 ) if q P =-1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)

  1. On the epistemic view of quantum states

    International Nuclear Information System (INIS)

    Skotiniotis, Michael; Roy, Aidan; Sanders, Barry C.

    2008-01-01

    We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens' toy model. We then test whether these axioms can be extended to capture more quantum phenomena by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxed definition of valid operations in Spekkens' toy model cannot produce an equivalence with the Clifford group for two qubits. However, the new operations do serve as tests for correlation in a two toy bit model, analogous to the well known Horodecki criterion for the separability of quantum states

  2. Experimental Realization of a Quantum Spin Pump

    DEFF Research Database (Denmark)

    Watson, Susan; Potok, R.; M. Marcus, C.

    2003-01-01

    We demonstrate the operation of a quantum spin pump based on cyclic radio-frequency excitation of a GaAs quantum dot, including the ability to pump pure spin without pumping charge. The device takes advantage of bidirectional mesoscopic fluctuations of pumped current, made spin-dependent by the a......We demonstrate the operation of a quantum spin pump based on cyclic radio-frequency excitation of a GaAs quantum dot, including the ability to pump pure spin without pumping charge. The device takes advantage of bidirectional mesoscopic fluctuations of pumped current, made spin......-dependent by the application of an in-plane Zeeman field. Spin currents are measured by placing the pump in a focusing geometry with a spin-selective collector....

  3. The entropic cost of quantum generalized measurements

    Science.gov (United States)

    Mancino, Luca; Sbroscia, Marco; Roccia, Emanuele; Gianani, Ilaria; Somma, Fabrizia; Mataloni, Paolo; Paternostro, Mauro; Barbieri, Marco

    2018-03-01

    Landauer's principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors.

  4. Fundamentals of quantum information

    International Nuclear Information System (INIS)

    Zeilinger, A.

    1998-01-01

    The fact that information is physical means that the laws of quantum mechanics can be used to process and transmit it in ways that are not possible with existing systems. Ever since its invention in the 1920s, quantum physics has given rise to countless discussions about its meaning and about how to interpret the theory correctly. These discussions focus on issues like the Einstein-Podolsky-Rosen paradox, quantum non-locality and the role of measurement in quantum physics. In recent years, however, research into the very foundations of quantum mechanics has also led to a new field quantum information technology. The use of quantum physics could revolutionize the way we communicate and process information. The important new observation is that information is not independent of the physical laws used to store and processes it (see Landauer in further reading). Although modern computers rely on quantum mechanics to operate, the information itself is still encoded classically. A new approach is to treat information as a quantum concept and to ask what new insights can be gained by encoding this information in individual quantum systems. In other words, what happens when both the transmission and processing of information are governed by quantum laws? (UK)

  5. Towards topological quantum computer

    Science.gov (United States)

    Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

    2018-01-01

    Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

  6. Towards topological quantum computer

    Directory of Open Access Journals (Sweden)

    D. Melnikov

    2018-01-01

    Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

  7. A formula for the Bloch vector of some Lindblad quantum systems

    International Nuclear Information System (INIS)

    Salgado, D.; Sanchez-Gomez, J.L.

    2004-01-01

    Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators

  8. Restoration for Noise Removal in Quantum Images

    Science.gov (United States)

    Liu, Kai; Zhang, Yi; Lu, Kai; Wang, Xiaoping

    2017-09-01

    Quantum computation has become increasingly attractive in the past few decades due to its extraordinary performance. As a result, some studies focusing on image representation and processing via quantum mechanics have been done. However, few of them have considered the quantum operations for images restoration. To address this problem, three noise removal algorithms are proposed in this paper based on the novel enhanced quantum representation model, oriented to two kinds of noise pollution (Salt-and-Pepper noise and Gaussian noise). For the first algorithm Q-Mean, it is designed to remove the Salt-and-Pepper noise. The noise points are extracted through comparisons with the adjacent pixel values, after which the restoration operation is finished by mean filtering. As for the second method Q-Gauss, a special mask is applied to weaken the Gaussian noise pollution. The third algorithm Q-Adapt is effective for the source image containing unknown noise. The type of noise can be judged through the quantum statistic operations for the color value of the whole image, and then different noise removal algorithms are used to conduct image restoration respectively. Performance analysis reveals that our methods can offer high restoration quality and achieve significant speedup through inherent parallelism of quantum computation.

  9. Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

    Science.gov (United States)

    Robinson, T. R.; Haven, E.

    2015-12-01

    Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

  10. Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

    International Nuclear Information System (INIS)

    Mostafazadeh, Ali

    2004-01-01

    With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂ t 2 +D)ψ(t)=0, where t is an element of R and D is a positive-definite operator acting in a Hilbert space H-tilde. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of H uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in H. Among these is a particular choice that generates t-translations in H and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in H, and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in L 2 R+L 2 R, show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the

  11. Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

    Science.gov (United States)

    Mostafazadeh, Ali

    2004-01-01

    With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂t2+D)ψ(t)=0, where t∈R and D is a positive-definite operator acting in a Hilbert space H~. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of H uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in H. Among these is a particular choice that generates t-translations in H and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in H, and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in L2(R)⊕L2(R), show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is

  12. Exceptional points in open quantum systems

    International Nuclear Information System (INIS)

    Mueller, Markus; Rotter, Ingrid

    2008-01-01

    Open quantum systems are embedded in the continuum of scattering wavefunctions and are naturally described by non-Hermitian Hamilton operators. In the complex energy plane, exceptional points appear at which two (or more) eigenvalues of the Hamilton operator coalesce. Although they are a countable set of single points in the complex energy plane and therefore of measure zero, they determine decisively the dynamics of open quantum systems. A powerful method for the description of open quantum systems is the Feshbach projection operator formalism. It is used in the present paper as a basic tool for the study of exceptional points and of the role they play for the dynamics of open quantum systems. Among others, the topological structure of the exceptional points, the rigidity of the phases of the eigenfunctions in their vicinity, the enhancement of observable values due to the reduced phase rigidity and the appearance of phase transitions are considered. The results are compared with existing experimental data on microwave cavities. In the last section, some questions being still unsolved, are considered

  13. Introduction to quantum graphs

    CERN Document Server

    Berkolaiko, Gregory

    2012-01-01

    A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...

  14. Quantum independent increment processes

    CERN Document Server

    Franz, Uwe

    2005-01-01

    This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

  15. Low voltage operation of electro-absorption modulator promising for high-definition 3D imaging application using a three step asymmetric coupled quantum well structure

    International Nuclear Information System (INIS)

    Na, Byung Hoon; Ju, Gun Wu; Cho, Yong Chul; Lee, Yong Tak; Choi, Hee Ju; Jeon, Jin Myeong; Lee, Soo Kyung; Park, Yong Hwa; Park, Chang Young

    2015-01-01

    In this paper, we propose a transmission type electro-absorption modulator (EAM) operating at 850 nm having low operating voltage and high absorption change with low insertion loss using a novel three step asymmetric coupled quantum well (3 ACQW) structure which can be used as an optical image shutter for high-definition (HD) three dimensional (3D) imaging. Theoretical calculations show that the exciton red shift of 3 ACQW structure is more than two times larger than that of rectangular quantum well (RQW) structure while maintaining high absorption change. The EAM having coupled cavities with 3 ACQW structure shows a wide spectral bandwidth and high amplitude modulation at a bias voltage of only -8V, which is 41% lower in operating voltage than that of RQW, making the proposed EAM highly attractive as an optical image shutter for HD 3D imaging applications

  16. Instantaneous Non-Local Computation of Low T-Depth Quantum Circuits

    DEFF Research Database (Denmark)

    Speelman, Florian

    2016-01-01

    -depth of a quantum circuit, able to perform non-local computation of quantum circuits with a (poly-)logarithmic number of layers of T gates with quasi-polynomial entanglement. Our proofs combine ideas from blind and delegated quantum computation with the garden-hose model, a combinatorial model of communication......Instantaneous non-local quantum computation requires multiple parties to jointly perform a quantum operation, using pre-shared entanglement and a single round of simultaneous communication. We study this task for its close connection to position-based quantum cryptography, but it also has natural...... applications in the context of foundations of quantum physics and in distributed computing. The best known general construction for instantaneous non-local quantum computation requires a pre-shared state which is exponentially large in the number of qubits involved in the operation, while efficient...

  17. Positive-Operator Valued Measure (POVM Quantization

    Directory of Open Access Journals (Sweden)

    Jean Pierre Gazeau

    2014-12-01

    Full Text Available We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on a normalized positive operator-valued measure. The latter are built from families of density operators labeled by points of the measure space. We especially focus on various probabilistic aspects of these constructions. Simple ormore elaborate examples illustrate the procedure: circle, two-sphere, plane and half-plane. Links with Positive-Operator Valued Measure (POVM quantum measurement and quantum statistical inference are sketched.

  18. Coherent states in quantum mechanics

    International Nuclear Information System (INIS)

    Rodrigues, R. de Lima; Fernandes Junior, Damasio; Batista, Sheyla Marques

    2001-12-01

    We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out. (author)

  19. The affine quantum gravity programme

    CERN Document Server

    Klauder, J R

    2002-01-01

    The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix left brace g-hat sub a sub b (x)right brace composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation relations are incompatible with this principle, and they must be replaced by noncanonical, affine commutation relations. Due to the partial second-class nature of the quantum gravitational constraints, it is advantageous to use the recently developed projection operator method, which treats all quantum constraints on an equal footing. Using this method, enforcement of regularized versions of the gravitational operator constraints is formulated quite naturally by means of a novel and relatively well-defined functional integral involving only the same set of variables that appears in the usual classical formulation. It is anticipated that skills and insight to study this formulation can be developed by studying special, reduced-variable models that sti...

  20. Concepts in quantum mechanics

    CERN Document Server

    Mathur, Vishnu S

    2008-01-01

    NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS Inadequacy of Classical Description for Small Systems Basis of Quantum Mechanics Representation of States Dual Vectors: Bra and Ket Vectors Linear Operators Adjoint of a Linear Operator Eigenvalues and Eigenvectors of a Linear Operator Physical Interpretation Observables and Completeness Criterion Commutativity and Compatibility of Observables Position and Momentum Commutation Relations Commutation Relation and the Uncertainty ProductAppendix: Basic Concepts in Classical MechanicsREPRESENTATION THEORY Meaning of Representation How to Set up a Representation Representatives of a Linear Operator Change of Representation Coordinate Representation Replacement of Momentum Observable p by -ih d/dqIntegral Representation of Dirac Bracket A2|F|A1> The Momentum Representation Dirac Delta FunctionRelation between the Coordinate and Momentum RepresentationsEQUATIONS OF MOTIONSchrödinger Equation of Motion Schrödinger Equation in the Coordinate Representation Equation o...