Li, Shu-Shen; Long, Gui-lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization.
Steane, A M
1998-01-01
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and qua...
2010-03-04
efficient or less costly than their classical counterparts. A large-scale quantum computer is certainly an extremely ambi- tious goal, appearing to us...outperform the largest classical supercomputers in solving some specific problems important for data encryption. In the long term, another application...which the quantum computer depends, causing the quantum mechanically destructive process known as decoherence . Decoherence comes in several forms
Ladd, T D; Jelezko, F; Laflamme, R; Nakamura, Y; Monroe, C; O'Brien, J L
2010-03-04
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.
Quantum Computing for Quantum Chemistry
2010-09-01
This three-year project consisted on the development and application of quantum computer algorithms for chemical applications. In particular, we developed algorithms for chemical reaction dynamics, electronic structure and protein folding. The first quantum computing for
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Duality Computing in Quantum Computers
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; LIU Yang
2008-01-01
In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.
Quantum robots and quantum computers
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Quantum Computing for Computer Architects
Metodi, Tzvetan
2011-01-01
Quantum computers can (in theory) solve certain problems far faster than a classical computer running any known classical algorithm. While existing technologies for building quantum computers are in their infancy, it is not too early to consider their scalability and reliability in the context of the design of large-scale quantum computers. To architect such systems, one must understand what it takes to design and model a balanced, fault-tolerant quantum computer architecture. The goal of this lecture is to provide architectural abstractions for the design of a quantum computer and to explore
Directory of Open Access Journals (Sweden)
Prashant Anil Patil
2012-04-01
Full Text Available This paper gives the detailed information about Quantum computer, and difference between quantum computer and traditional computers, the basis of Quantum computers which are slightly similar but still different from traditional computer. Many research groups are working towards the highly technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. Quantum computer is very much use full for computation purpose in field of Science and Research. Large amount of data and information will be computed, processing, storing, retrieving, transmitting and displaying information in less time with that much of accuracy which is not provided by traditional computers.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article,we make a review on the development of a newly proposed quantum computer,duality computer,or the duality quantum computer and the duality mode of quantum computers.The duality computer is based on the particle-wave duality principle of quantum mechanics.Compared to an ordinary quantum computer,the duality quantum computer is a quantum computer on the move and passing through a multi-slit.It offers more computing operations than is possible with an ordinary quantum computer.The most two distinct operations are:the quantum division operation and the quantum combiner operation.The division operation divides the wave function of a quantum computer into many attenuated,and identical parts.The combiner operation combines the wave functions in different parts into a single part.The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer.The main structure of duality quantum computer and duality mode,the duality mode,their mathematical description and algorithm designs are reviewed.
National Research Council Canada - National Science Library
Jeremy L. O'Brien
2007-01-01
In 2001, all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single-photon sources, linear optical elements, and single-photon detectors...
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Introduction to Quantum Computation
Ekert, A.
A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.
Kendon, Vivien M; Nemoto, Kae; Munro, William J
2010-08-13
We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.
Introduction to quantum computers
Berman, Gennady P; Mainieri, Ronnie; Tsifrinovich, Vladimir I
1998-01-01
Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shorâ€™s algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by im
Simulation of quantum computers
De Raedt, H; Michielsen, K; Hams, AH; Miyashita, S; Saito, K; Landau, DP; Lewis, SP; Schuttler, HB
2001-01-01
We describe a simulation approach to study the functioning of Quantum Computer hardware. The latter is modeled by a collection of interacting spin-1/2 objects. The time evolution of this spin system maps one-to-one to a quantum program carried out by the Quantum Computer. Our simulation software con
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2009-01-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e., joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Preskill, J
1997-01-01
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 10^6 qubits, with a probability of error per quantum gate of order 10^{-6}, would be a formidable factoring engine. Even a smaller, less accurate quantum computer would be able to perform many useful tasks. (This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18 December 1996.)
Quantum computing classical physics.
Meyer, David A
2002-03-15
In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice-gas automata--and show how to implement them efficiently on standard quantum computers.
Quantum Computation and Quantum Spin Dynamics
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
Quantum Computation and Quantum Spin Dynamics
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
Probabilistic Cloning and Quantum Computation
Institute of Scientific and Technical Information of China (English)
GAO Ting; YAN Feng-Li; WANG Zhi-Xi
2004-01-01
@@ We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which the cloning offers an advantage which cannot be matched by any approach that does not resort to quantum cloning.In these quantum computations, we need to distribute quantum information contained in the states about which we have some partial information. To perform quantum computations, we use a state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.
Explorations in quantum computing
Williams, Colin P
2011-01-01
By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. ""Quantum computing"" is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers -- and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking suppos
Algorithms for Quantum Computers
Smith, Jamie
2010-01-01
This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of quantum Fourier transform based algorithms, followed by quantum searching and some of its early generalizations. It continues with a more in-depth description of two more recent developments: algorithms developed in the quantum walk paradigm, followed by tensor network evaluation algorithms (which include approximating the Tutte polynomial).
Blind Quantum Signature with Blind Quantum Computation
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.
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2016-12-01
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.
Quantum Computational Cryptography
Kawachi, Akinori; Koshiba, Takeshi
As computational approaches to classical cryptography have succeeded in the establishment of the foundation of the network security, computational approaches even to quantum cryptography are promising, since quantum computational cryptography could offer richer applications than the quantum key distribution. Our project focused especially on the quantum one-wayness and quantum public-key cryptosystems. The one-wayness of functions (or permutations) is one of the most important notions in computational cryptography. First, we give an algorithmic characterization of quantum one-way permutations. In other words, we show a necessary and sufficient condition for quantum one-way permutations in terms of reflection operators. Second, we introduce a problem of distinguishing between two quantum states as a new underlying problem that is harder to solve than the graph automorphism problem. The new problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. We show that the problem has several cryptographic properties and they enable us to construct a quantum publickey cryptosystem, which is likely to withstand any attack of a quantum adversary.
Zak, M.
1998-01-01
Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.
Quantum computing with trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.
1998-01-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
2011-12-01
an inspiring speech at the MIT Physics of Computation 1st Conference in 1981, Feynman proposed the development of a computer that would obey the...on ion trap based 36 quantum computing for physics and computer science students would include lecture notes, slides, lesson plans, a syllabus...reading lists, videos, demonstrations, and laboratories. 37 LIST OF REFERENCES [1] R. P. Feynman , “Simulating physics with computers,” Int. J
Concurrent Quantum Computation
Yamaguchi, F; Yamamoto, Y
2000-01-01
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to produce a computational result is stored in the phase shifts of the 2^n arms. They can be detected by interferometry that allows us to utilize quantum parallelism. Quantum algorithms are accountable for what interferometers to be constructed to compute particular problems. A standard formalism for constructing the arms has been developed by the extension of classical reversible gate arrays. By its nature of sequential applications of logic operations, the required number of gates increases exponentially as the problem size grows. This may cause a crucial obstacle to perform a quantum computation within a limited decoherence time. We propose a direct and concurrent construction of the interferometer arms by one-time evolution of a physical system with arbitrary multi-particle i...
Quantum computing: towards reality
Trabesinger, Andreas
2017-03-01
The concept of computers that harness the laws of quantum mechanics has transformed our thinking about how information can be processed. Now the environment exists to make prototype devices a reality.
Lobe, Elisabeth; Stollenwerk, Tobias; Tröltzsch, Anke
2015-01-01
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic ...
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
Pinski, Sebastian D
2011-01-01
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.
O'Brien, Jeremy L
2007-12-07
In 2001, all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single-photon sources, linear optical elements, and single-photon detectors. Although it was in principle scalable, the massive resource overhead made the scheme practically daunting. However, several simplifications were followed by proof-of-principle demonstrations, and recent approaches based on cluster states or error encoding have dramatically reduced this worrying resource overhead, making an all-optical architecture a serious contender for the ultimate goal of a large-scale quantum computer. Key challenges will be the realization of high-efficiency sources of indistinguishable single photons, low-loss, scalable optical circuits, high-efficiency single-photon detectors, and low-loss interfacing of these components.
Introduction to topological quantum matter & quantum computation
Stanescu, Tudor D
2017-01-01
What is -topological- about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-know...
Quantum probabilistically cloning and computation
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article we make a review on the usefulness of probabilistically cloning and present examples of quantum computation tasks for which quantum cloning offers an advantage which cannot be matched by any approach that does not resort to it.In these quantum computations,one needs to distribute quantum information contained in states about which we have some partial information.To perform quantum computations,one uses state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.And we discuss the achievable efficiencies and the efficient quantum logic network for probabilistic cloning the quantum states used in implementing quantum computation tasks for which cloning provides enhancement in performance.
Abstract quantum computing machines and quantum computational logics
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
2016-06-01
Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.
Demonstration of blind quantum computing.
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip
2012-01-20
Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.
Basic concepts in quantum computation
Ekert, A K; Inamori, H; Ekert, Artur; Hayden, Patrick; Inamori, Hitoshi
2000-01-01
Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional quantum dynamics 11 Decoherence and recoherence 12 Concluding remarks
Quantum Mobile Crypto-Computation
Institute of Scientific and Technical Information of China (English)
XIONGYan; CHENHuanhuan; GUNaijie; MIAOFuyou
2005-01-01
In this paper, a quantum approach for solving the mobile crypto-computation problem is proposed. In our approach, quantum signature and quantum entanglement have been employed to strengthen the security of mobile computation. Theory analysis shows that our solution is secure against classic and quantum attacks.
Holographic quantum computing.
Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus
2008-07-25
We propose to use a single mesoscopic ensemble of trapped polar molecules for quantum computing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields.
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
Aharonov, D; Kempe, J; Landau, Z; Lloyd, S; Regev, O; Aharonov, Dorit; Dam, Wim van; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded
2004-01-01
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum circuit model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models provides a new vantage point from which to tackle the central issues in quantum computation, namely designing new quantum algorithms and constructing fault tolerant quantum computers. In particular, by translating the main open questions in quantum algorithms to the language of spectral gaps of sparse matrices, the result makes quantum algorithmic questions accessible to a wider scientific audience, acquainted with mathematical physics, expander theory a...
Quantum Computation Toward Quantum Gravity
Zizzi, P. A.
2001-08-01
The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin -1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.
Quantum Computation and Spin Electronics
DiVincenzo, David P.; Burkard, Guido; Loss, Daniel; Sukhorukov, Eugene V.
1999-01-01
In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics. We discuss five ...
Arrighi, P; Arrighi, Pablo; Salvail, Louis
2003-01-01
We investigate the possibility of having someone carry out the work of executing a function for you, but without letting him learn anything about your input. Say Alice wants Bob to compute some well-known function f upon her input x, but wants to prevent Bob from learning anything about x. The situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute f(x) "blindly", i.e. without observing x? We provide such a blind computation protocol for the class of functions which admit an efficient procedure to generate random input-output pairs, e.g. factorization. The setting is quantum, the security is unconditional, the eavesdropper is as malicious as can be. Keywords: Secure Circuit Evaluation, Secure Two-party Computation, Information Hiding, Information gain vs disturbance.
Short Introduction to Quantum Computation
2007-11-02
Proceedings of the Air Force Office of Scientific Research Computational Mathematics Meeting 1996 Revision 2 Short Introduction to Quantum...useful for nanoscale computing and quantum computing. KEY WORDS: quantum computing, nano-scale computing, Moore’s law 1 Introduction It is likely that...memory) Digital Devices magnetostrictive delay line Intel 1103 integrated circuit IBM 3340 disk drive Smallest DRAM cell reported on at ISSC Current
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only...... the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...
Quantum computing of semiclassical formulas.
Georgeot, B; Giraud, O
2008-04-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
Quantum Computing, Metrology, and Imaging
Lee, H; Dowling, J P; Lee, Hwang; Lougovski, Pavel; Dowling, Jonathan P.
2005-01-01
Information science is entering into a new era in which certain subtleties of quantum mechanics enables large enhancements in computational efficiency and communication security. Naturally, precise control of quantum systems required for the implementation of quantum information processing protocols implies potential breakthoughs in other sciences and technologies. We discuss recent developments in quantum control in optical systems and their applications in metrology and imaging.
Quantum computing on encrypted data.
Fisher, K A G; Broadbent, A; Shalm, L K; Yan, Z; Lavoie, J; Prevedel, R; Jennewein, T; Resch, K J
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Quantum computing on encrypted data
Fisher, K. A. G.; Broadbent, A.; Shalm, L. K.; Yan, Z.; Lavoie, J.; Prevedel, R.; Jennewein, T.; Resch, K. J.
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Quantum computer for dummies (in Russian)
Grozin, Andrey
2011-01-01
An introduction (in Russian) to quantum computers, quantum cryptography, and quantum teleportation for students who have no previous knowledge of these subjects, but know quantum mechanics. Several simple examples are considered in detail using the quantum computer emulator QCL.
Programmable architecture for quantum computing
Chen, J.; Wang, L.; Charbon, E.; Wang, B.
2013-01-01
A programmable architecture called “quantum FPGA (field-programmable gate array)” (QFPGA) is presented for quantum computing, which is a hybrid model combining the advantages of the qubus system and the measurement-based quantum computation. There are two kinds of buses in QFPGA, the local bus and t
Fluxon-controlled quantum computer
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2016-11-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e. joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Programmable architecture for quantum computing
Chen, J.; Wang, L.; Charbon, E.; Wang, B.
2013-01-01
A programmable architecture called “quantum FPGA (field-programmable gate array)” (QFPGA) is presented for quantum computing, which is a hybrid model combining the advantages of the qubus system and the measurement-based quantum computation. There are two kinds of buses in QFPGA, the local bus and t
Quantum computing with defects.
Weber, J R; Koehl, W F; Varley, J B; Janotti, A; Buckley, B B; Van de Walle, C G; Awschalom, D D
2010-05-11
Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantum computer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV(-1)) center stands out for its robustness--its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV(-1) center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors.
Layered Architecture for Quantum Computing
National Research Council Canada - National Science Library
Jones, N. Cody; Van Meter, Rodney; Fowler, Austin G; McMahon, Peter L; Kim, Jungsang; Ladd, Thaddeus D; Yamamoto, Yoshihisa
2012-01-01
.... 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...
Quantum computing: Efficient fault tolerance
Gottesman, Daniel
2016-12-01
Dealing with errors in a quantum computer typically requires complex programming and many additional quantum bits. A technique for controlling errors has been proposed that alleviates both of these problems.
Hypercomputation based on quantum computing
Sicard, A; Ospina, J; Sicard, Andr\\'es; V\\'elez, Mario; Ospina, Juan
2004-01-01
We present a quantum algorithm for a (classically) incomputable decision problem: the Hilbert's tenth problem; namely, we present a hypercomputation model based on quantum computation. The model is inspired by the one proposed by Tien D. Kieu. Our model exploits the quantum adiabatic process and the characteristics of the representation of the dynamical algebra su(1,1) associated to the infinite square well. Furthermore, it is demonstrated that the model proposed is a universal quantum computation model.
Addition on a Quantum Computer
Draper, Thomas G
2000-01-01
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register. This method also allows for massive parallelization in its execution.
Interfacing external quantum devices to a universal quantum computer.
Lagana, Antonio A; Lohe, Max A; von Smekal, Lorenz
2011-01-01
We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer.
Interfacing external quantum devices to a universal quantum computer.
Directory of Open Access Journals (Sweden)
Antonio A Lagana
Full Text Available We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer.
Massively parallel quantum computer simulator
De Raedt, K.; Michielsen, K.; De Raedt, H.; Trieu, B.; Arnold, G.; Richter, M.; Lippert, Th.; Watanabe, H.; Ito, N.
2007-01-01
We describe portable software to simulate universal quantum computers on massive parallel Computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray
Towards quantum chemistry on a quantum computer.
Lanyon, B P; Whitfield, J D; Gillett, G G; Goggin, M E; Almeida, M P; Kassal, I; Biamonte, J D; Mohseni, M; Powell, B J; Barbieri, M; Aspuru-Guzik, A; White, A G
2010-02-01
Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.
Fault-tolerant quantum computation
Preskill, J
1997-01-01
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.
Vianna, R O; Monken, C H; Vianna, Reinaldo O.; Rabelo, Wilson R. M.
2003-01-01
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure classical architecture, no matter how few qubits are available and, therefore, it suggests an easier implementable technology than a pure quantum computer with arbitrary number of qubits.
Energy Technology Data Exchange (ETDEWEB)
Koenneker, Carsten (comp.)
2012-11-01
The following topics are dealt with: Reality in the test facility, quantum teleportation, the reality of quanta, interaction-free quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view in the future of quantum optics. (HSI)
Quantum Computing over Finite Fields
James, Roshan P; Sabry, Amr
2011-01-01
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a finite field instead of the field of complex numbers. This instantiation collapses much the structure of actual quantum mechanics but retains several of its distinguishing characteristics including the notions of superposition, interference, and entanglement. Furthermore, discrete quantum theory excludes local hidden variable models, has a no-cloning theorem, and can express natural counterparts of quantum information protocols such as superdense coding and teleportation. Our first result is to distill a model of discrete quantum computing from this quantum theory. The model is expressed using a monadic metalanguage built on top of a universal reversible language for finite computations, and hence is directly implementab...
Simulating chemistry using quantum computers
Kassal, Ivan; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán
2010-01-01
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
Simulating chemistry using quantum computers.
Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán
2011-01-01
The difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
Algorithms on ensemble quantum computers.
Boykin, P Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh
2010-06-01
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and σ(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.
Quantum information processing in nanostructures Quantum optics; Quantum computing
Reina-Estupinan, J H
2002-01-01
Since information has been regarded os a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, 'nanostructures', through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of ...
Models of optical quantum computing
Directory of Open Access Journals (Sweden)
Krovi Hari
2017-03-01
Full Text Available I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.
Quantum Computer Using Coupled Quantum Dot Molecules
Wu, N J; Natori, A; Yasunaga, H; Wu*, Nan-Jian
1999-01-01
We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can...
Quasicrystals and Quantum Computing
Berezin, Alexander A.
1997-03-01
In Quantum (Q) Computing qubits form Q-superpositions for macroscopic times. One scheme for ultra-fast (Q) computing can be based on quasicrystals. Ultrafast processing in Q-coherent structures (and the very existence of durable Q-superpositions) may be 'consequence' of presence of entire manifold of integer arithmetic (A0, aleph-naught of Georg Cantor) at any 4-point of space-time, furthermore, at any point of any multidimensional phase space of (any) N-particle Q-system. The latter, apart from quasicrystals, can include dispersed and/or diluted systems (Berezin, 1994). In such systems such alleged centrepieces of Q-Computing as ability for fast factorization of long integers can be processed by sheer virtue of the fact that entire infinite pattern of prime numbers is instantaneously available as 'free lunch' at any instant/point. Infinitely rich pattern of A0 (including pattern of primes and almost primes) acts as 'independent' physical effect which directly generates Q-dynamics (and physical world) 'out of nothing'. Thus Q-nonlocality can be ultimately based on instantaneous interconnectedness through ever- the-same structure of A0 ('Platonic field' of integers).
The Physics of Quantum Computation
Falci, Giuseppe; Paladino, Elisabette
2015-10-01
Quantum Computation has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. QC has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. In these lecture notes we focus on physical hardware, present day challenges and future directions for design of quantum architectures.
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
Arvind
2001-02-01
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically
Quantum computing in neural networks
Gralewicz, P
2004-01-01
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits. This raises the possibility of a large-scale quantum computing using PMs, especially with neural networks which have the innate capability for probabilistic information processing. Restricting ourselves to a particular model, we construct and numerically examine the performance of neural circuits implementing universal quantum gates. A discussion on the physiological plausibility of proposed coding scheme is also provided.
Quantum Computation Beyond the Circuit Model
Jordan, Stephen P.
2008-01-01
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a ge...
Cryptography, quantum computation and trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, Richard J.
1998-03-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
Universal blind quantum computation for hybrid system
Huang, He-Liang; Bao, Wan-Su; Li, Tan; Li, Feng-Guang; Fu, Xiang-Qun; Zhang, Shuo; Zhang, Hai-Long; Wang, Xiang
2017-08-01
As progress on the development of building quantum computer continues to advance, first-generation practical quantum computers will be available for ordinary users in the cloud style similar to IBM's Quantum Experience nowadays. Clients can remotely access the quantum servers using some simple devices. In such a situation, it is of prime importance to keep the security of the client's information. Blind quantum computation protocols enable a client with limited quantum technology to delegate her quantum computation to a quantum server without leaking any privacy. To date, blind quantum computation has been considered only for an individual quantum system. However, practical universal quantum computer is likely to be a hybrid system. Here, we take the first step to construct a framework of blind quantum computation for the hybrid system, which provides a more feasible way for scalable blind quantum computation.
Experimental quantum computing without entanglement.
Lanyon, B P; Barbieri, M; Almeida, M P; White, A G
2008-11-14
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.
Quantum information and computing
Ohya, M; Watanabe, N
2006-01-01
The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of ?-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum
Computing on Anonymous Quantum Network
Kobayashi, Hirotada; Tani, Seiichiro
2010-01-01
This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolea...
Quantum-enhanced Sensing and Efficient Quantum Computation
2015-07-27
Quantum -enhanced sensing and efficient quantum computation Ian Walmsley THE UNIVERSITY OF...COVERED (From - To) 1 February 2013 - 31 January 2015 4. TITLE AND SUBTITLE Quantum -enhanced sensing and efficient quantum computation 5a. CONTRACT...1895616013 Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18 Final report for “ Quantum ‐Enhanced Sensing and Efficient Quantum Computation
Quantum Computing via The Bethe Ansatz
Zhang, Yong,
2011-01-01
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a para...
Kesidis, George
2009-01-01
Wong's diffusion network is a stochastic, zero-input Hopfield network with a Gibbs stationary distribution over a bounded, connected continuum. Previously, logarithmic thermal annealing was demonstrated for the diffusion network and digital versions of it were studied and applied to imaging. Recently, "quantum" annealed Markov chains have garnered significant attention because of their improved performance over "pure" thermal annealing. In this note, a joint quantum and thermal version of Wong's diffusion network is described and its convergence properties are studied. Different choices for "auxiliary" functions are discussed, including those of the kinetic type previously associated with quantum annealing.
Massive Parallel Quantum Computer Simulator
De Raedt, K; De Raedt, H; Ito, N; Lippert, T; Michielsen, K; Richter, M; Trieu, B; Watanabe, H; Lippert, Th.
2006-01-01
We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a function of the number of processors and suggest that the simulation software described in this paper may also serve as benchmark for testing high-end parallel computers.
Continuous Quantum Computation
2007-03-01
Eigenvalues and Eigenvectors”, by D.S. Abrams and S. Lloyd Physical Review Letters , 1999, Vol. 83, 5162-5156 [6] “Design of Strongly Modulating...by Y.S. Weinstein, S.Lloyd, J.V. Emerson and D.G. Cory, Physical Review Letters , 2002, Vol. 89,157902 [8] “The Edge of Quantum Chaos”, by Y.S...Weinstein, S. Lloyd and C. Tsallis, Physical Review Letters , 2002, Vol. 89, 214101 [9] “Fidelity Decay as an Efficient Indicator of Quantum Chaos
Delegating private quantum computations12
Broadbent, Anne
2015-09-01
We give a protocol for the delegation of quantum computation on encrypted data. More specifically, we show that in a client-server scenario, where the client holds the encryption key for an encrypted quantum register held by the server, it is possible for the server to perform a universal set of quantum gates on the quantum data. All Clifford group gates are non-interactive, while the remaining non-Clifford group gate that we implement (the p/8 gate) requires the client to prepare and send a single random auxiliary qubit (chosen among four possibilities), and exchange classical communication. This construction improves on previous work, which requires either multiple auxiliary qubits or two-way quantum communication. Using a reduction to an entanglement-based protocol, we show privacy against any adversarial server according to a simulation-based security definition.
QCE : A Simulator for Quantum Computer Hardware
Michielsen, Kristel; Raedt, Hans De
2003-01-01
The Quantum Computer Emulator (QCE) described in this paper consists of a simulator of a generic, general purpose quantum computer and a graphical user interface. The latter is used to control the simulator, to define the hardware of the quantum computer and to debug and execute quantum algorithms.
DEFF Research Database (Denmark)
Salvail, Louis; Arrighi, Pablo
2006-01-01
protocol for the class of functions which admit an efficient procedure to generate random input-output pairs, e.g. factorization. The cheat-sensitive security achieved relies only upon quantum theory being true. The security analysis carried out assumes the eavesdropper performs individual attacks....
Cavity QED: applications to quantum computation
Xiong, Han; Zubairy, M. Suhail
2004-10-01
Possible schemes to implement the basic quantum gates for quantum computation have been presented based on cavity quantum electrodynamics (QED) systems. We then discuss schemes to implement several important quantum algorithms such as the discrete quantum fourier transform (QFT) algorithm and Grover's quantum search algorithm based on these quantum gates. Some other applications of cavity QED based systems including the implementations of a quantum disentanglement eraser and an entanglement amplifier are also discussed.
Handbook of computational quantum chemistry
Cook, David B
2005-01-01
Quantum chemistry forms the basis of molecular modeling, a tool widely used to obtain important chemical information and visual images of molecular systems. Recent advances in computing have resulted in considerable developments in molecular modeling, and these developments have led to significant achievements in the design and synthesis of drugs and catalysts. This comprehensive text provides upper-level undergraduates and graduate students with an introduction to the implementation of quantum ideas in molecular modeling, exploring practical applications alongside theoretical explanations.Wri
Using a quantum computer to investigate quantum chaos
Schack, Ruediger
1997-01-01
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Adiabatic quantum computation along quasienergies
Tanaka, Atushi
2009-01-01
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of...
Quantum Walks for Computer Scientists
Venegas-Andraca, Salvador
2008-01-01
Quantum computation, one of the latest joint ventures between physics and the theory of computation, is a scientific field whose main goals include the development of hardware and algorithms based on the quantum mechanical properties of those physical systems used to implement such algorithms. Solving difficult tasks (for example, the Satisfiability Problem and other NP-complete problems) requires the development of sophisticated algorithms, many of which employ stochastic processes as their mathematical basis. Discrete random walks are a popular choice among those stochastic processes. Inspir
Reversible computing fundamentals, quantum computing, and applications
De Vos, Alexis
2010-01-01
Written by one of the few top internationally recognized experts in the field, this book concentrates on those topics that will remain fundamental, such as low power computing, reversible programming languages, and applications in thermodynamics. It describes reversible computing from various points of view: Boolean algebra, group theory, logic circuits, low-power electronics, communication, software, quantum computing. It is this multidisciplinary approach that makes it unique.Backed by numerous examples, this is useful for all levels of the scientific and academic community, from undergr
Atomic physics: A milestone in quantum computing
Bartlett, Stephen D.
2016-08-01
Quantum computers require many quantum bits to perform complex calculations, but devices with more than a few bits are difficult to program. A device based on five atomic quantum bits shows a way forward. See Letter p.63
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)
Phase Information in Quantum Oracle Computing
Machta, J.
1998-01-01
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmissio...
ASCR Workshop on Quantum Computing for Science
Energy Technology Data Exchange (ETDEWEB)
Aspuru-Guzik, Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Van Dam, Wim [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Farhi, Edward [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Gaitan, Frank [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Humble, Travis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jordan, Stephen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Landahl, Andrew J [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Love, Peter [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lucas, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Preskill, John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Muller, Richard P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Svore, Krysta [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wiebe, Nathan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Williams, Carl [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-06-01
This report details the findings of the DOE ASCR Workshop on Quantum Computing for Science that was organized to assess the viability of quantum computing technologies to meet the computational requirements of the DOE’s science and energy mission, and to identify the potential impact of quantum technologies. The workshop was held on February 17-18, 2015, in Bethesda, MD, to solicit input from members of the quantum computing community. The workshop considered models of quantum computation and programming environments, physical science applications relevant to DOE's science mission as well as quantum simulation, and applied mathematics topics including potential quantum algorithms for linear algebra, graph theory, and machine learning. This report summarizes these perspectives into an outlook on the opportunities for quantum computing to impact problems relevant to the DOE’s mission as well as the additional research required to bring quantum computing to the point where it can have such impact.
Quantum Computation: Entangling with the Future
Jiang, Zhang
2017-01-01
Commercial applications of quantum computation have become viable due to the rapid progress of the field in the recent years. Efficient quantum algorithms are discovered to cope with the most challenging real-world problems that are too hard for classical computers. Manufactured quantum hardware has reached unprecedented precision and controllability, enabling fault-tolerant quantum computation. Here, I give a brief introduction on what principles in quantum mechanics promise its unparalleled computational power. I will discuss several important quantum algorithms that achieve exponential or polynomial speedup over any classical algorithm. Building a quantum computer is a daunting task, and I will talk about the criteria and various implementations of quantum computers. I conclude the talk with near-future commercial applications of a quantum computer.
Barium Ions for Quantum Computation
Dietrich, M R; Bowler, R; Kurz, N; Salacka, J S; Shu, G; Blinov, B B
2009-01-01
Individually trapped 137Ba+ in an RF Paul trap is proposed as a qubit ca ndidate, and its various benefits are compared to other ionic qubits. We report the current experimental status of using this ion for quantum computation. Fut ure plans and prospects are discussed.
An Early Quantum Computing Proposal
Energy Technology Data Exchange (ETDEWEB)
Lee, Stephen Russell [Los Alamos National Laboratory; Alexander, Francis Joseph [Los Alamos National Laboratory; Barros, Kipton Marcos [Los Alamos National Laboratory; Daniels, Marcus G. [Los Alamos National Laboratory; Gattiker, James R. [Los Alamos National Laboratory; Hamada, Michael Scott [Los Alamos National Laboratory; Howse, James Walter [Los Alamos National Laboratory; Loncaric, Josip [Los Alamos National Laboratory; Pakin, Scott D. [Los Alamos National Laboratory; Somma, Rolando Diego [Los Alamos National Laboratory; Vernon, Louis James [Los Alamos National Laboratory
2016-04-04
The D-Wave 2X is the third generation of quantum processing created by D-Wave. NASA (with Google and USRA) and Lockheed Martin (with USC), both own D-Wave systems. Los Alamos National Laboratory (LANL) purchased a D-Wave 2X in November 2015. The D-Wave 2X processor contains (nominally) 1152 quantum bits (or qubits) and is designed to specifically perform quantum annealing, which is a well-known method for finding a global minimum of an optimization problem. This methodology is based on direct execution of a quantum evolution in experimental quantum hardware. While this can be a powerful method for solving particular kinds of problems, it also means that the D-Wave 2X processor is not a general computing processor and cannot be programmed to perform a wide variety of tasks. It is a highly specialized processor, well beyond what NNSA currently thinks of as an “advanced architecture.”A D-Wave is best described as a quantum optimizer. That is, it uses quantum superposition to find the lowest energy state of a system by repeated doses of power and settling stages. The D-Wave produces multiple solutions to any suitably formulated problem, one of which is the lowest energy state solution (global minimum). Mapping problems onto the D-Wave requires defining an objective function to be minimized and then encoding that function in the Hamiltonian of the D-Wave system. The quantum annealing method is then used to find the lowest energy configuration of the Hamiltonian using the current D-Wave Two, two-level, quantum processor. This is not always an easy thing to do, and the D-Wave Two has significant limitations that restrict problem sizes that can be run and algorithmic choices that can be made. Furthermore, as more people are exploring this technology, it has become clear that it is very difficult to come up with general approaches to optimization that can both utilize the D-Wave and that can do better than highly developed algorithms on conventional computers for
Experimental realization of nonadiabatic holonomic quantum computation.
Feng, Guanru; Xu, Guofu; Long, Guilu
2013-05-10
Because of its geometric nature, holonomic quantum computation is fault tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantum computation in a liquid NMR quantum information processor. Two noncommuting one-qubit holonomic gates, rotations about x and z axes, and the two-qubit holonomic CNOT gate are realized by evolving the work qubits and an ancillary qubit nonadiabatically. The successful realizations of these universal elementary gates in nonadiabatic holonomic quantum computation demonstrates the experimental feasibility of this quantum computing paradigm.
Quantum Chromodynamics: Computational Aspects
Schaefer, Thomas
2016-01-01
We present a brief introduction to QCD, the QCD phase diagram, and non-equilibrium phenomena in QCD. We emphasize aspects of the theory that can be addressed using computational methods, in particular euclidean path integral Monte Carlo, fluid dynamics, kinetic theory, classical field theory and holographic duality.
General Quantum Interference Principle and Duality Computer
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu
2006-01-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of thesub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer,the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer,it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented:the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
Quantum mechanics and computation; Quanta y Computacion
Energy Technology Data Exchange (ETDEWEB)
Cirac Sasturain, J. I.
2000-07-01
We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs.
Problems and solutions in quantum computing and quantum information
Steeb, Willi-Hans
2012-01-01
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, deportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, number states and Bose operators, coherent states, squeezed states, Gaussian states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton opera...
Classical computing, quantum computing, and Shor's factoring algorithm
Manin, Yu I
1999-01-01
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the P/NP problem are reviewed. Section 2 introduces the notion of quantum parallelism and explains the main issues of quantum computing. Section 3 is devoted to four quantum subroutines: initialization, quantum computing of classical Boolean functions, quantum Fourier transform, and Grover's search algorithm. The central Section 4 explains Shor's factoring algorithm. Section 5 relates Kolmogorov's complexity to the spectral properties of computable function. Appendix contributes to the prehistory of quantum computing.
Strange attractor simulated on a quantum computer
2002-01-01
We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature.
Experimental demonstration of blind quantum computing
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joe; Zeilinger, Anton; Walther, Philip
2012-02-01
Quantum computers are among the most promising applications of quantum-enhanced technologies. Quantum effects such as superposition and entanglement enable computational speed-ups that are unattainable using classical computers. The challenges in realising quantum computers suggest that in the near future, only a few facilities worldwide will be capable of operating such devices. In order to exploit these computers, users would seemingly have to give up their privacy. It was recently shown that this is not the case and that, via the universal blind quantum computation protocol, quantum mechanics provides a way to guarantee that the user's data remain private. Here, we demonstrate the first experimental version of this protocol using polarisation-entangled photonic qubits. We demonstrate various blind one- and two-qubit gate operations as well as blind versions of the Deutsch's and Grover's algorithms. When the technology to build quantum computers becomes available, this will become an important privacy-preserving feature of quantum information processing.
Experimental Demonstration of Blind Quantum Computing
Barz, Stefanie; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip
2011-01-01
Quantum computers, besides offering substantial computational speedups, are also expected to provide the possibility of preserving the privacy of a computation. Here we show the first such experimental demonstration of blind quantum computation where the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. We demonstrate various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover algorithms. Remarkably, the client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for future unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.
Quantum computing and the entanglement frontier
Preskill, John
2012-01-01
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantum computer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantum computer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state sy...
Quantum Computation and Decision Trees
Farhi, E; Farhi, Edward; Gutmann, Sam
1998-01-01
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root. We devise a quantum mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level n in time polynomial in n, then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in n, but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
Geometry of quantum computation with qutrits.
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.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Optically simulated universal quantum computation
Francisco, D.; Ledesma, S.
2008-04-01
Recently, classical optics based systems to emulate quantum information processing have been proposed. The analogy is based on the possibility of encoding a quantum state of a system with a 2N-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a certain basis is associated with the complex amplitude of the electromagnetic field in a given slice of the laser wavefront. Temporal evolution is represented as the change of the complex amplitude of the field when the wavefront pass through a certain optical arrangement. Different modules that represent universal gates for quantum computation have been implemented. For instance, unitary operations acting on the qbits space (or U(2) gates) are represented by means of two phase plates, two spherical lenses and a phase grating in a typical image processing set up. In this work, we present CNOT gates which are emulated by means of a cube prism that splits a pair of adjacent rays incoming from the input image. As an example of application, we present an optical module that can be used to simulate the quantum teleportation process. We also show experimental results that illustrate the validity of the analogy. Although the experimental results obtained are promising and show the capability of the system for simulate the real quantum process, we must take into account that any classical simulation of quantum phenomena, has as fundamental limitation the impossibility of representing non local entanglement. In this classical context, quantum teleportation has only an illustrative interpretation.
Brain Neurons as Quantum Computers:
Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.
The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.
Diamond NV centers for quantum computing and quantum networks
Childress, L.; Hanson, R.
2013-01-01
The exotic features of quantum mechanics have the potential to revolutionize information technologies. Using superposition and entanglement, a quantum processor could efficiently tackle problems inaccessible to current-day computers. Nonlocal correlations may be exploited for intrinsically secure co
Exploiting Locality in Quantum Computation for Quantum Chemistry.
McClean, Jarrod R; Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-12-18
Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.
Quantum Computation with Nonlinear Optics
Liu, Yang; Zhang, Wen-Hong; Zhang, Cun-Lin; Long, Gui-Lu
2008-01-01
We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features: (1) No auxiliary qubits are required in the controlled-NOT gate operation; (2) No measurement is required in the course of the computation; (3) It is resource efficient and conceptually simple.
Quantum Computation with Nonlinear Optics
Institute of Scientific and Technical Information of China (English)
LU Ke; LIU Yang; LIN Zhen-Quan; ZHANG Wen-Hong; SUN Yun-Fei; ZHANG Cun-Lin; LONG Gui-Lu
2008-01-01
We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features: (1) No auxiliary qubits are required in the controlled-NOT gate operation; (2) No measurement is required in the courseof the computation; (3) It is resource efficient and conceptually simple.
Quantum ballistic evolution in quantum mechanics application to quantum computers
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 pr...
EXPLORATIONS IN QUANTUM COMPUTING FOR FINANCIAL APPLICATIONS
Gare, Jesse
2010-01-01
Quantum computers have the potential to increase the solution speed for many computational problems. This paper is a first step into possible applications for quantum computing in the context of computational finance. The fundamental ideas of quantum computing are introduced, followed by an exposition of the algorithms of Deutsch and Grover. Improved mean and median estimation are shown as results of Grover?s generalized framework. The algorithm for mean estimation is refined to an improved M...
Holonomic Quantum Computation in Subsystems
Oreshkov, Ognyan
2009-08-01
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
Holonomic quantum computation in subsystems
Oreshkov, Ognyan
2009-01-01
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
Toward a superconducting quantum computer. Harnessing macroscopic quantum coherence.
Tsai, Jaw-Shen
2010-01-01
Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still many new research opportunities open to physicists and engineers.
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Elucidating reaction mechanisms on quantum computers.
Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias
2017-07-18
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
Experimental one-way quantum computing.
Walther, P; Resch, K J; Rudolph, T; Schenck, E; Weinfurter, H; Vedral, V; Aspelmeyer, M; Zeilinger, A
2005-03-10
Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.
Quantum machine learning what quantum computing means to data mining
Wittek, Peter
2014-01-01
Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine L
Adiabatic quantum computation and quantum annealing theory and practice
McGeoch, Catherine C
2014-01-01
Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov
Quantum Computing with Very Noisy Devices
Knill, E
2004-01-01
There are quantum algorithms that can efficiently simulate quantum physics, factor large numbers and estimate integrals. As a result, quantum computers can solve otherwise intractable computational problems. One of the main problems of experimental quantum computing is to preserve fragile quantum states in the presence of errors. It is known that if the needed elementary operations (gates) can be implemented with error probabilities below a threshold, then it is possible to efficiently quantum compute with arbitrary accuracy. Here we give evidence that for independent errors the theoretical threshold is well above 3%, which is a significant improvement over that of earlier calculations. However, the resources required at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum algorithms at error probabil...
The Quantum Human Computer (QHC) Hypothesis
Salmani-Nodoushan, Mohammad Ali
2008-01-01
This article attempts to suggest the existence of a human computer called Quantum Human Computer (QHC) on the basis of an analogy between human beings and computers. To date, there are two types of computers: Binary and Quantum. The former operates on the basis of binary logic where an object is said to exist in either of the two states of 1 and…
Universal quantum computation with qudits
Luo, MingXing; Wang, XiaoJun
2014-09-01
Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm. Most of previous algorithms are based on the qubit systems. Herein a proposal for a universal circuit is given based on the qudit system, which is larger and can store more information. In order to prove its universality for quantum applications, an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation. The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions. In comparison to previous quantum qudit logical gates, each primitive qudit gate is only dependent on two free parameters and may be easily implemented. In experimental implementation, multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates. The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.
Energy-efficient quantum computing
Ikonen, Joni; Salmilehto, Juha; Möttönen, Mikko
2017-04-01
In the near future, one of the major challenges in the realization of large-scale quantum computers operating at low temperatures is the management of harmful heat loads owing to thermal conduction of cabling and dissipation at cryogenic components. This naturally raises the question that what are the fundamental limitations of energy consumption in scalable quantum computing. In this work, we derive the greatest lower bound for the gate error induced by a single application of a bosonic drive mode of given energy. Previously, such an error type has been considered to be inversely proportional to the total driving power, but we show that this limitation can be circumvented by introducing a qubit driving scheme which reuses and corrects drive pulses. Specifically, our method serves to reduce the average energy consumption per gate operation without increasing the average gate error. Thus our work shows that precise, scalable control of quantum systems can, in principle, be implemented without the introduction of excessive heat or decoherence.
Parallel computing and quantum chromodynamics
Bowler, K C
1999-01-01
The study of Quantum Chromodynamics (QCD) remains one of the most challenging topics in elementary particle physics. The lattice formulation of QCD, in which space-time is treated as a four- dimensional hypercubic grid of points, provides the means for a numerical solution from first principles but makes extreme demands upon computational performance. High Performance Computing (HPC) offers us the tantalising prospect of a verification of QCD through the precise reproduction of the known masses of the strongly interacting particles. It is also leading to the development of a phenomenological tool capable of disentangling strong interaction effects from weak interaction effects in the decays of one kind of quark into another, crucial for determining parameters of the standard model of particle physics. The 1980s saw the first attempts to apply parallel architecture computers to lattice QCD. The SIMD and MIMD machines used in these pioneering efforts were the ICL DAP and the Cosmic Cube, respectively. These wer...
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
Model dynamics for quantum computing
Tabakin, Frank
2017-08-01
A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.
Embracing the quantum limit in silicon computing.
Morton, John J L; McCamey, Dane R; Eriksson, Mark A; Lyon, Stephen A
2011-11-16
Quantum computers hold the promise of massive performance enhancements across a range of applications, from cryptography and databases to revolutionary scientific simulation tools. Such computers would make use of the same quantum mechanical phenomena that pose limitations on the continued shrinking of conventional information processing devices. Many of the key requirements for quantum computing differ markedly from those of conventional computers. However, silicon, which plays a central part in conventional information processing, has many properties that make it a superb platform around which to build a quantum computer.
Decoherence, Control, and Symmetry in Quantum Computers
Bacon, D J
2003-01-01
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such collective decoherence decoherence-free encodings is demonstrated. Rigorous definitions of control and the use of encoded universality in quantum computers are addressed. Explicit gate constructions for encoded universality on ion trap and exchange based quantum computers are given. In the second part of the thesis we examine physical systems with error correcting properties. We examine systems that can store quantum infor...
On the computation of quantum characteristic exponents
Vilela-Mendes, R; Coutinho, Ricardo
1998-01-01
A quantum characteristic exponent may be defined, with the same operational meaning as the classical Lyapunov exponent when the latter is expressed as a functional of densities. Existence conditions and supporting measure properties are discussed as well as the problems encountered in the numerical computation of the quantum exponents. Although an example of true quantum chaos may be exhibited, the taming effect of quantum mechanics on chaos is quite apparent in the computation of the quantum exponents. However, even when the exponents vanish, the functionals used for their definition may still provide a characterization of distinct complexity classes for quantum behavior.
Contextuality supplies the 'magic' for quantum computation.
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-19
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.
Helping Students Learn Quantum Mechanics for Quantum Computing
Singh, Chandralekha
2016-01-01
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
Quantum fields on the computer
1992-01-01
This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.
Distributed Quantum Computation over Noisy Channels
Ekert, A K; Macchiavello, C; Cirac, J I
1999-01-01
We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. We show that for a sufficiently large number of nodes maximally entangled states are always advantageous over independent computations in each node, even in the presence of noise during the computation process.
Quantum computation with two-dimensional graphene quantum dots
Institute of Scientific and Technical Information of China (English)
Li Jie-Sen; Li Zhi-Bing; Yao Dao-Xin
2012-01-01
We study an array of graphene nano sheets that form a two-dimensional S =1/2 Kagome spin lattice used for quantum computation.The edge states of the graphene nano sheets axe used to form quantum dots to confine electrons and perform the computation.We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots.It is shown that both schemes contain a great amount of information for quantum computation.The corresponding gate operations are also proposed.
Quantum Computing in Solid State Systems
Ruggiero, B; Granata, C
2006-01-01
The aim of Quantum Computation in Solid State Systems is to report on recent theoretical and experimental results on the macroscopic quantum coherence of mesoscopic systems, as well as on solid state realization of qubits and quantum gates. Particular attention has been given to coherence effects in Josephson devices. Other solid state systems, including quantum dots, optical, ion, and spin devices which exhibit macroscopic quantum coherence are also discussed. Quantum Computation in Solid State Systems discusses experimental implementation of quantum computing and information processing devices, and in particular observations of quantum behavior in several solid state systems. On the theoretical side, the complementary expertise of the contributors provides models of the various structures in connection with the problem of minimizing decoherence.
An introduction to reliable quantum computation
Aliferis, Panos
2011-01-01
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.
Quantum computing. Defining and detecting quantum speedup.
Rønnow, Troels F; Wang, Zhihui; Job, Joshua; Boixo, Sergio; Isakov, Sergei V; Wecker, David; Martinis, John M; Lidar, Daniel A; Troyer, Matthias
2014-07-25
The development of small-scale quantum devices raises the question of how to fairly assess and detect quantum speedup. Here, we show how to define and measure quantum speedup and how to avoid pitfalls that might mask or fake such a speedup. We illustrate our discussion with data from tests run on a D-Wave Two device with up to 503 qubits. By using random spin glass instances as a benchmark, we found no evidence of quantum speedup when the entire data set is considered and obtained inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results do not rule out the possibility of speedup for other classes of problems and illustrate the subtle nature of the quantum speedup question.
Quantum computing with incoherent resources and quantum jumps.
Santos, M F; Cunha, M Terra; Chaves, R; Carvalho, A R R
2012-04-27
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that, when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify this by showing how to efficiently prepare graph states for the implementation of measurement-based quantum computation.
Prospects for quantum computation with trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.; James, D.F.V.
1997-12-31
Over the past decade information theory has been generalized to allow binary data to be represented by two-state quantum mechanical systems. (A single two-level system has come to be known as a qubit in this context.) The additional freedom introduced into information physics with quantum systems has opened up a variety of capabilities that go well beyond those of conventional information. For example, quantum cryptography allows two parties to generate a secret key even in the presence of eavesdropping. But perhaps the most remarkable capabilities have been predicted in the field of quantum computation. Here, a brief survey of the requirements for quantum computational hardware, and an overview of the in trap quantum computation project at Los Alamos are presented. The physical limitations to quantum computation with trapped ions are discussed.
Disciplines, models, and computers: the path to computational quantum chemistry.
Lenhard, Johannes
2014-12-01
Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990.
Quantum computing with realistically noisy devices.
Knill, E
2005-03-03
In theory, quantum computers offer a means of solving problems that would be intractable on conventional computers. Assuming that a quantum computer could be constructed, it would in practice be required to function with noisy devices called 'gates'. These gates cause decoherence of the fragile quantum states that are central to the computer's operation. The goal of so-called 'fault-tolerant quantum computing' is therefore to compute accurately even when the error probability per gate (EPG) is high. Here we report a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent. Such EPGs have been experimentally demonstrated, but to avoid excessive resource overheads required by the necessary architecture, lower EPGs are needed. Assuming the availability of quantum resources comparable to the digital resources available in today's computers, we show that non-trivial quantum computations at EPGs of as high as one per cent could be implemented.
Multilayer microwave integrated quantum circuits for scalable quantum computing
Brecht, Teresa; Pfaff, Wolfgang; Wang, Chen; Chu, Yiwen; Frunzio, Luigi; Devoret, Michel H.; Schoelkopf, Robert J.
2016-02-01
As experimental quantum information processing (QIP) rapidly advances, an emerging challenge is to design a scalable architecture that combines various quantum elements into a complex device without compromising their performance. In particular, superconducting quantum circuits have successfully demonstrated many of the requirements for quantum computing, including coherence levels that approach the thresholds for scaling. However, it remains challenging to couple a large number of circuit components through controllable channels while suppressing any other interactions. We propose a hardware platform intended to address these challenges, which combines the advantages of integrated circuit fabrication and the long coherence times achievable in three-dimensional circuit quantum electrodynamics. This multilayer microwave integrated quantum circuit platform provides a path towards the realisation of increasingly complex superconducting devices in pursuit of a scalable quantum computer.
Computational quantum-classical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
2016-05-18
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Nonlinear optics quantum computing with circuit QED.
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.
The one-way quantum computer - a non-network model of quantum computation
Raussendorf, R; Briegel, H J; Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J.
2001-01-01
A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)
An overview of quantum computation models: quantum automata
Institute of Scientific and Technical Information of China (English)
2008-01-01
Quantum automata,as theoretical models of quantum computers,include quantum finite automata (QFA),quantum sequential machines (QSM),quantum pushdown automata (QPDA),quantum Turing machines (QTM),quantum cellular automata (QCA),and the others,for example,automata theory based on quantum logic (orthomodular lattice-valued automata).In this paper,we try to outline a basic progress in the research on these models,focusing on QFA,QSM,QPDA,QTM,and orthomodular lattice-valued automata.Also,other models closely relative to them are mentioned.In particular,based on the existing results in the literature,we finally address a number of problems to be studied in future.
Quantum state diffusion, localization and computation
Schack, R; Percival, I C
1995-01-01
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage of the localization of quantum states into wave packets occupying small regions of classical phase space. Following and extending the original proposal of Percival, Alber and Steimle, we show that MQSD can provide a further gain over ordinary QSD and other quantum trajectory methods of many orders of magnitude in computational space and time. Because of these gains, it is even possible to calculate an open quantum system trajectory when the corresponding isolated system is intractable. MQSD is particularly advantageous where classical or semiclassical dynamics provides an adequate qualitative picture but is numerically inaccurate because of significant quantum effects. The principles are illustrated by computations for the quantum Duffing oscillator and for second harmonic...
Distributed measurement-based quantum computation
Danos, V; Kashefi, E; Panangaden, P; Danos, Vincent; Hondt, Ellie D'; Kashefi, Elham; Panangaden, Prakash
2005-01-01
We develop a formal model for distributed measurement-based quantum computations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need to model it as a global structure, reminiscent of global memory in classical agent systems. Local quantum computations are described as measurement patterns. Since measurement-based quantum computation is inherently distributed, this allows us to extend naturally several concepts of the measurement calculus, a formal model for such computations. Our goal is to define an assembly language, i.e. we assume that computations are well-defined and we do not concern ourselves with verification techniques. The operational semantics for systems of agents is given by a probabilistic transition system, and we define operational equivalence in a way that it corresponds to the notion of bisimilarity. With this in place, we prove that teleportation is bisimilar to a direct quantum channe...
The potential of the quantum computer
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...
Quantum computer of wire circuit architecture
Moiseev, S A; Andrianov, S N
2010-01-01
First solid state quantum computer was built using transmons (cooper pair boxes). The operation of the computer is limited because of using a number of the rigit cooper boxes working with fixed frequency at temperatures of superconducting material. Here, we propose a novel architecture of quantum computer based on a flexible wire circuit of many coupled quantum nodes containing controlled atomic (molecular) ensembles. We demonstrate wide opportunities of the proposed computer. Firstly, we reveal a perfect storage of external photon qubits to multi-mode quantum memory node and demonstrate a reversible exchange of the qubits between any arbitrary nodes. We found optimal parameters of atoms in the circuit and self quantum modes for quantum processing. The predicted perfect storage has been observed experimentally for microwave radiation on the lithium phthalocyaninate molecule ensemble. Then also, for the first time we show a realization of the efficient basic two-qubit gate with direct coupling of two arbitrary...
Adiabatic Quantum Computation: Coherent Control Back Action
Goswami, Debabrata
2013-01-01
Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments. PMID:23788822
Quantum Computing: Linear Optics Implementations
Sundsøy, Pål
2016-01-01
One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probabilit...
Quantum Genetic Algorithms for Computer Scientists
Rafael Lahoz-Beltra
2016-01-01
Genetic algorithms (GAs) are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data) has led to a new class of GAs known as “Quantum Geneti...
On the completeness of quantum computation models
Arrighi, Pablo
2010-01-01
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to define an absolute notion of completeness for quantum computation models and give a precise meaning to the Church-Turing thesis in the framework of quantum theory. (Extra keywords: quantum programming languages, denotational semantics, universality.)
Quantum computation architecture using optical tweezers
DEFF Research Database (Denmark)
Weitenberg, Christof; Kuhr, Stefan; Mølmer, Klaus;
2011-01-01
We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits...... quantum computing....
Quantum computer: an appliance for playing market games
Piotrowski, Edward W.; Jan Sladkowski
2003-01-01
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game theory. The paper contain an analysis of such markets that shows that there would be advantage in using quantum computers and quantum strategies.
Adiabatic quantum computation and quantum phase transitions
Latorre, J I; Latorre, Jose Ignacio; Orus, Roman
2003-01-01
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.
Simulated Quantum Computation of Molecular Energies
Aspuru-Guzik, A; Love, P J; Head-Gordon, M; Aspuru-Guzik, Al\\'an; Dutoi, Anthony D.; Love, Peter J.; Head-Gordon, Martin
2005-01-01
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.
Performing quantum computing experiments in the cloud
Devitt, Simon J.
2016-09-01
Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.
Computing a Turing-Incomputable Problem from Quantum Computing
Sicard, A; Ospina, J; Sicard, Andr\\'es; V\\'elez, Mario; Ospina, Juan
2003-01-01
A hypercomputation model named Infinite Square Well Hypercomputation Model (ISWHM) is built from quantum computation. This model is inspired by the model proposed by Tien D. Kieu quant-ph/0203034 and solves an Turing-incomputable problem. For the proposed model and problem, a simulation of its behavior is made. Furthermore, it is demonstrated that ISWHM is a universal quantum computation model.
Universal quantum computation with little entanglement.
Van den Nest, Maarten
2013-02-01
We show that universal quantum computation can be achieved in the standard pure-state circuit model while the entanglement entropy of every bipartition is small in each step of the computation. The entanglement entropy required for large-scale quantum computation even tends to zero. Moreover we show that the same conclusion applies to many entanglement measures commonly used in the literature. This includes e.g., the geometric measure, localizable entanglement, multipartite concurrence, squashed entanglement, witness-based measures, and more generally any entanglement measure which is continuous in a certain natural sense. These results demonstrate that many entanglement measures are unsuitable tools to assess the power of quantum computers.
Teleportation of Two Quantum States via the Quantum Computation
Institute of Scientific and Technical Information of China (English)
FENG Mang; ZHU Xi-Wen; FANG Xi-Ming; YAN Min; SHI Lei
2000-01-01
A scheme of teleportation of two unknown quantum states via quantum computation is proposed. The comparison with the former proposals shows that our scheme is more in tune with the original teleportation proposal and the effciency is higher. The teleportation of an unknown entangled state is also discussed.
Numerical characteristics of quantum computer simulation
Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.
2016-12-01
The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.
Quantum Computation Using Optically Coupled Quantum Dot Arrays
Pradhan, Prabhakar; Anantram, M. P.; Wang, K. L.; Roychowhury, V. P.; Saini, Subhash (Technical Monitor)
1998-01-01
A solid state model for quantum computation has potential advantages in terms of the ease of fabrication, characterization, and integration. The fundamental requirements for a quantum computer involve the realization of basic processing units (qubits), and a scheme for controlled switching and coupling among the qubits, which enables one to perform controlled operations on qubits. We propose a model for quantum computation based on optically coupled quantum dot arrays, which is computationally similar to the atomic model proposed by Cirac and Zoller. In this model, individual qubits are comprised of two coupled quantum dots, and an array of these basic units is placed in an optical cavity. Switching among the states of the individual units is done by controlled laser pulses via near field interaction using the NSOM technology. Controlled rotations involving two or more qubits are performed via common cavity mode photon. We have calculated critical times, including the spontaneous emission and switching times, and show that they are comparable to the best times projected for other proposed models of quantum computation. We have also shown the feasibility of accessing individual quantum dots using the NSOM technology by calculating the photon density at the tip, and estimating the power necessary to perform the basic controlled operations. We are currently in the process of estimating the decoherence times for this system; however, we have formulated initial arguments which seem to indicate that the decoherence times will be comparable, if not longer, than many other proposed models.
Computational security of quantum encryption
Alagic, G.; Broadbent, A.; Fefferman, B.; Gagliardoni, T.; Schaffner, C.; St. Jules, M.; Nascimento, A.C.A.; Barreto, P.
2016-01-01
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of
Numerical computation for teaching quantum statistics
Price, Tyson; Swendsen, Robert H.
2013-11-01
The study of ideal quantum gases reveals surprising quantum effects that can be observed in macroscopic systems. The properties of bosons are particularly unusual because a macroscopic number of particles can occupy a single quantum state. We describe a computational approach that supplements the usual analytic derivations applicable in the thermodynamic limit. The approach involves directly summing over the quantum states for finite systems and avoids the need for doing difficult integrals. The results display the unusual behavior of quantum gases even for relatively small systems.
Hyper-parallel photonic quantum computation with coupled quantum dots
Ren, Bao-Cang; Deng, Fu-Guo
2014-01-01
It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility of achieving scalable hyper-parallel quantum computation based on two DOFs of photon systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both the spatial-mode and the polarization DOFs of a two-photon system simultaneously, by exploiting the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics (QED). This hyper-CNOT gate is implemented by manipulating the four qubits in the two DOFs of a two-photon system without auxiliary spatial modes or polarization modes. It reduces the operation time and the resources consumed in quantum information processing, and it is more robust against the photonic dissipation noise, compared with the integration of several cascaded CNOT gates in one DOF. PMID:24721781
Conceptual aspects of geometric quantum computation
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Effective pure states for bulk quantum computation
Energy Technology Data Exchange (ETDEWEB)
Knill, E.; Chuang, I.; Laflamme, R.
1997-11-01
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) and Corey et al. (spatial averaging) for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla qubits and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high temperature and low temperature bulk quantum computing and analyze the signal to noise behavior of each.
Quantum Computing with Electron Spins in Quantum Dots
Vandersypen, L M K; Van Beveren, L H W; Elzerman, J M; Greidanus, J S; De Franceschi, S; Kouwenhoven, Leo P
2002-01-01
We present a set of concrete and realistic ideas for the implementation of a small-scale quantum computer using electron spins in lateral GaAs/AlGaAs quantum dots. Initialization is based on leads in the quantum Hall regime with tunable spin-polarization. Read-out hinges on spin-to-charge conversion via spin-selective tunneling to or from the leads, followed by measurement of the number of electron charges on the dot via a charge detector. Single-qubit manipulation relies on a microfabricated wire located close to the quantum dot, and two-qubit interactions are controlled via the tunnel barrier connecting the respective quantum dots. Based on these ideas, we have begun a series of experiments in order to demonstrate unitary control and to measure the coherence time of individual electron spins in quantum dots.
Fault tolerant quantum computation with nondeterministic gates.
Li, Ying; Barrett, Sean D; Stace, Thomas M; Benjamin, Simon C
2010-12-17
In certain approaches to quantum computing the operations between qubits are nondeterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should be assumed to be failure prone. In the ultimate limit of this architecture each component contains only one qubit. Here we derive thresholds for fault-tolerant quantum computation under this extreme paradigm. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded; meanwhile the rate of unknown errors should not exceed 2 in 10(4) operations.
Measurement Based Quantum Computation on Fractal Lattices
Directory of Open Access Journals (Sweden)
Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Non-Mechanism in Quantum Oracle Computing
Castagnoli, G C
1999-01-01
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As well known, some oracle problems are solved more efficiently by using quantum algorithms; this naturally implies changing the computer to quantum, while the choice of the software program remains sharp. In order to highlight the non-mechanistic origin of this higher efficiency, also the uncertainty about which program is installed must be represented in a quantum way.
Quantum Computation explained to my Mother
Arrighi, P
2003-01-01
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the shortest of the latter category. The aim is to deliver a short yet rigorous and self-contained introduction to Quantum Computation, whilst assuming the reader has no prior knowledge of anything but the fundamental operations on real numbers. Successively I introduce complex matrices; the postulates of quantum theory and the simplest quantum algorithm. The document originates from a fifty minutes talk addressed to a non-specialist audience, in which I sought to take the shortest mathematical path that proves a quantum algorithm right.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Materials Frontiers to Empower Quantum Computing
Energy Technology Data Exchange (ETDEWEB)
Taylor, Antoinette Jane [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sarrao, John Louis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Richardson, Christopher [Laboratory for Physical Sciences, College Park, MD (United States)
2015-06-11
This is an exciting time at the nexus of quantum computing and materials research. The materials frontiers described in this report represent a significant advance in electronic materials and our understanding of the interactions between the local material and a manufactured quantum state. Simultaneously, directed efforts to solve materials issues related to quantum computing provide an opportunity to control and probe the fundamental arrangement of matter that will impact all electronic materials. An opportunity exists to extend our understanding of materials functionality from electronic-grade to quantum-grade by achieving a predictive understanding of noise and decoherence in qubits and their origins in materials defects and environmental coupling. Realizing this vision systematically and predictively will be transformative for quantum computing and will represent a qualitative step forward in materials prediction and control.
Reducing computational complexity of quantum correlations
Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal
2015-12-01
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures such as quantum discord and quantum work deficit in two qubits and higher-dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having nonpositive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.
Experimental comparison of two quantum computing architectures
Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A.; Wright, Kenneth; Monroe, Christopher
2017-01-01
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future. PMID:28325879
Is the Brain a Quantum Computer?
Litt, Abninder; Eliasmith, Chris; Kroon, Frederick W.; Weinstein, Steven; Thagard, Paul
2006-01-01
We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic…
Experimental comparison of two quantum computing architectures.
Linke, Norbert M; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A; Wright, Kenneth; Monroe, Christopher
2017-03-28
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www. ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.
Directional coupling for quantum computing and communication.
Nikolopoulos, Georgios M
2008-11-14
We introduce the concept of directional coupling, i.e., the selective transfer of a state between adjacent quantum wires, in the context of quantum computing and communication. Our analysis rests upon a mathematical analogy between a dual-channel directional coupler and a composite spin system.
An introduction to quantum computing algorithms
Pittenger, Arthur O
2000-01-01
In 1994 Peter Shor [65] published a factoring algorithm for a quantum computer that finds the prime factors of a composite integer N more efficiently than is possible with the known algorithms for a classical com puter. Since the difficulty of the factoring problem is crucial for the se curity of a public key encryption system, interest (and funding) in quan tum computing and quantum computation suddenly blossomed. Quan tum computing had arrived. The study of the role of quantum mechanics in the theory of computa tion seems to have begun in the early 1980s with the publications of Paul Benioff [6]' [7] who considered a quantum mechanical model of computers and the computation process. A related question was discussed shortly thereafter by Richard Feynman [35] who began from a different perspec tive by asking what kind of computer should be used to simulate physics. His analysis led him to the belief that with a suitable class of "quantum machines" one could imitate any quantum system.
Scaling ion traps for quantum computing
CSIR Research Space (South Africa)
Uys, H
2010-09-01
Full Text Available The design, fabrication and preliminary testing of a chipscale, multi-zone, surface electrode ion trap is reported. The modular design and fabrication techniques used are anticipated to advance scalability of ion trap quantum computing architectures...
Optimised resource construction for verifiable quantum computation
Kashefi, Elham; Wallden, Petros
2017-04-01
Recent developments have brought the possibility of achieving scalable quantum networks and quantum devices closer. From the computational point of view these emerging technologies become relevant when they are no longer classically simulatable. Hence a pressing challenge is the construction of practical methods to verify the correctness of the outcome produced by universal or non-universal quantum devices. A promising approach that has been extensively explored is the scheme of verification via encryption through blind quantum computation. We present here a new construction that simplifies the required resources for any such verifiable protocol. We obtain an overhead that is linear in the size of the input (computation), while the security parameter remains independent of the size of the computation and can be made exponentially small (with a small extra cost). Furthermore our construction is generic and could be applied to any universal or non-universal scheme with a given underlying graph.
Universality of Black Hole Quantum Computing
Dvali, Gia; Lust, Dieter; Omar, Yasser; Richter, Benedikt
2016-01-01
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 e...
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONGGui－Lu; YANHai－Yang; 等
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the "state" of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.
Delayed Commutation in Quantum Computer Networks
García-Escartín, Juan Carlos; Chamorro-Posada, Pedro
2006-09-01
In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communication. We propose a nonclassical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes, we can route a qubit packet after part of it has left the network node.
Delayed commutation in quantum computer networks
Garcia-Escartin, J C; Chamorro-Posada, Pedro; Garcia-Escartin, Juan Carlos
2005-01-01
In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communications. We propose a non-classical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes we can route the information after part of it has left the network node.
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Quantum Computing and Shor`s Factoring Algorithm
Volovich, Igor V.
2001-01-01
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm. Factoring integers. NP-complete problems.
Private quantum computation: an introduction to blind quantum computing and related protocols
Fitzsimons, Joseph F.
2017-06-01
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.
EDITORIAL: Quantum Computing and the Feynman Festival
Brandt, Howard E.; Kim, Young S.; Man'ko, Margarita A.
2003-12-01
The Feynman Festival is a new interdisciplinary conference developed for studying Richard Feynman and his physics. The first meeting of this new conference series was held at the University of Maryland on 23--28 August 2002 (http://www.physics.umd.edu/robot/feynman.html) and the second meeting is scheduled for August 2004 at the same venue. According to Feynman, the different aspects of nature are different aspects of the same thing. Therefore, the ultimate purpose of the conference is to find Feynman's same thing from all different theories. For this reason, the first meeting of the Festival did not begin with a fixed formula, but composed its scientific programme based on responses from the entire physics community. The conference drew the most enthusiastic response from the community of quantum computing, the field initiated by Feynman. Encouraged by the response, we decided to edit a special issue of Journal of Optics B: Quantum and Semiclassical Optics on quantum computing in connection with the first Feynman Festival. The authorship is not restricted to the participants of the Feynman Festival, and all interested parties were encouraged to submit their papers on this subject. Needless to say, all the papers were peer reviewed according to the well-established standards of the journal. The subject of quantum computing is not restricted to building and operating computers. It requires a deeper understanding of how quantum mechanics works in materials as well as in our minds. Indeed, it covers the basic foundations of quantum mechanics, measurement theory, information theory, quantum optics, atomic physics and condensed matter physics. It may be necessary to develop new mathematical tools to accommodate the language that nature speaks. It is gratifying to note that this special issue contains papers covering all these aspects of quantum computing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one
Superadiabatic holonomic quantum computation in cavity QED
Liu, Bao-Jie; Huang, Zhen-Hua; Xue, Zheng-Yuan; Zhang, Xin-Ding
2017-06-01
Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition requires that the process be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited coherent times of the quantum systems. Here, we propose a feasible scheme to implement universal holonomic quantum computation based on non-Abelian geometric phases with superadiabatic quantum control, where the adiabatic manipulation is sped up while retaining its robustness against errors in the timing control. Consolidating the advantages of both strategies, our proposal is thus both robust and fast. The cavity QED system is adopted as a typical example to illustrate the merits where the proposed scheme can be realized in a tripod configuration by appropriately controlling the pulse shapes and their relative strength. To demonstrate the distinct performance of our proposal, we also compare our scheme with the conventional adiabatic strategy.
Fundamental gravitational limitations to quantum computing
Gambini, R; Pullin, J; Gambini, Rodolfo; Porto, Rafael A.; Pullin, Jorge
2005-01-01
Lloyd has considered the ultimate limitations physics places on quantum computers. He concludes in particular that for an ``ultimate laptop'' (a computer of one liter of volume and one kilogram of mass) the maximum number of operations per second is bounded by $10^{51}$. The limit is derived considering ordinary quantum mechanics. Here we consider additional limits that are placed by quantum gravity ideas, namely the use of a relational notion of time and fundamental gravitational limits that exist on time measurements. We then particularize for the case of an ultimate laptop and show that the maximum number of operations is further constrained to $10^{47}$ per second.
Natural and artificial atoms for quantum computation
Energy Technology Data Exchange (ETDEWEB)
Buluta, Iulia; Ashhab, Sahel; Nori, Franco, E-mail: fnori@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama, 351-0198 (Japan)
2011-10-15
Remarkable progress towards realizing quantum computation has been achieved using natural and artificial atoms as qubits. This paper presents a brief overview of the current status of different types of qubits. On the one hand, natural atoms (such as neutral atoms and ions) have long coherence times, and could be stored in large arrays, providing ideal 'quantum memories'. On the other hand, artificial atoms (such as superconducting circuits or semiconductor quantum dots) have the advantage of custom-designed features and could be used as 'quantum processing units'. Natural and artificial atoms can be coupled with each other and can also be interfaced with photons for long-distance communications. Hybrid devices made of natural/artificial atoms and photons may provide the next-generation design for quantum computers.
Quantum Fourier transform in computational basis
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
Brain-Computer Interfaces and Quantum Robots
Pessa, Eliano
2009-01-01
The actual (classical) Brain-Computer Interface attempts to use brain signals to drive suitable actuators performing the actions corresponding to subject's intention. However this goal is not fully reached, and when BCI works, it does only in particular situations. The reason of this unsatisfactory result is that intention cannot be conceived simply as a set of classical input-output relationships. It is therefore necessary to resort to quantum theory, allowing the occurrence of stable coherence phenomena, in turn underlying high-level mental processes such as intentions and strategies. More precisely, within the context of a dissipative Quantum Field Theory of brain operation it is possible to introduce generalized coherent states associated, within the framework of logic, to the assertions of a quantum metalanguage. The latter controls the quantum-mechanical computing corresponding to standard mental operation. It thus become possible to conceive a Quantum Cyborg in which a human mind controls, through a qu...
Cat-qubits for quantum computation
Mirrahimi, Mazyar
2016-08-01
The development of quantum Josephson circuits has created a strong expectation for reliable processing of quantum information. While this progress has already led to various proof-of-principle experiments on small-scale quantum systems, a major scaling step is required towards many-qubit protocols. Fault-tolerant computation with protected logical qubits usually comes at the expense of a significant overhead in the hardware. Each of the involved physical qubits still needs to satisfy the best achieved properties (coherence times, coupling strengths and tunability). Here, and in the aim of addressing alternative approaches to deal with these obstacles, I overview a series of recent theoretical proposals, and the experimental developments following these proposals, to enable a hardware-efficient paradigm for quantum memory protection and universal quantum computation. xml:lang="fr"
Robust dynamical decoupling for quantum computing and quantum memory.
Souza, Alexandre M; Alvarez, Gonzalo A; Suter, Dieter
2011-06-17
Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.
Quantum algorithms for computational nuclear physics
Directory of Open Access Journals (Sweden)
Višňák Jakub
2015-01-01
Full Text Available While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei for its possible practical realization on a real quantum computer.
Quantum Genetic Algorithms for Computer Scientists
Directory of Open Access Journals (Sweden)
Rafael Lahoz-Beltra
2016-10-01
Full Text Available Genetic algorithms (GAs are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data has led to a new class of GAs known as “Quantum Genetic Algorithms” (QGAs. In this review, we present a discussion, future potential, pros and cons of this new class of GAs. The review will be oriented towards computer scientists interested in QGAs “avoiding” the possible difficulties of quantum-mechanical phenomena.
Elements of quantum computing history, theories and engineering applications
Akama, Seiki
2015-01-01
A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's, and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation, and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers. This book provides a quick introduction to quantum computing for readers who have no backgrounds of both theory of computation and quantum mechanics. “Elements of Quantum Computing” presents the history, theories, and engineering applications of quantum computing. The book is suitable to computer scientists, physicist, and software engineers.
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)
Compressed quantum computation using a remote five-qubit quantum computer
Hebenstreit, M.; Alsina, D.; Latorre, J. I.; Kraus, B.
2017-05-01
The notion of compressed quantum computation is employed to simulate the Ising interaction of a one-dimensional chain consisting of n qubits using the universal IBM cloud quantum computer running on log2(n ) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer with a limited amount of runs. As a solution, we propose to use validating circuits, that is, to run independent controlled quantum circuits of similar complexity to the circuit of interest.
Efficient quantum circuits for one-way quantum computing.
Tanamoto, Tetsufumi; Liu, Yu-Xi; Hu, Xuedong; Nori, Franco
2009-03-13
While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenberg model. Our approach thus makes one-way quantum computing more feasible for solid-state devices.
Free spin quantum computation with semiconductor nanostructures
Zhang, W M; Soo, C; Zhang, Wei-Min; Wu, Yin-Zhong; Soo, Chopin
2005-01-01
Taking the excess electron spin in a unit cell of semiconductor multiple quantum-dot structure as a qubit, we can implement scalable quantum computation without resorting to spin-spin interactions. The technique of single electron tunnelings and the structure of quantum-dot cellular automata (QCA) are used to create a charge entangled state of two electrons which is then converted into spin entanglement states by using single spin rotations. Deterministic two-qubit quantum gates can also be manipulated using only single spin rotations with help of QCA. A single-short read-out of spin states can be realized by coupling the unit cell to a quantum point contact.
Universality of Entanglement and Quantum Computation Complexity
Orus, R; Orus, Roman; Latorre, Jose I.
2004-01-01
We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The analytic result for Shor's algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore difficulting the possibility of an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution Exact Cover algorithm, which also shows universality of the quantum phase transition the system evolves nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains a bounded quantity even at the critical point. A classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.
Progress in theoretical quantum computing
Institute of Scientific and Technical Information of China (English)
2008-01-01
@@ Computing is perhaps one of the most distinguished features that differentiate humans from animals.Aside from counting numbers using fingers and toes,abacus was the first great computing machine of human civilization.
Quantum Computation by Pairing Trapped Ultracold Ions
Institute of Scientific and Technical Information of China (English)
冯芒; 朱熙文; 高克林; 施磊
2001-01-01
Superpositional wavefunction oscillations for the implementation of quantum algorithms modify the desired interference required for the quantum computation. We propose a scheme with trapped ultracold ion-pairs beingqubits to diminish the detrimental effect of the wavefunction oscillations, which is applied to the two-qubitGrover's search. It can be also found that the qubits in our scheme are more robust against the decoherencecaused by the environment, and the model is scalable.
Entanglement and Quantum Computation: An Overview
Energy Technology Data Exchange (ETDEWEB)
Perez, R.B.
2000-06-27
This report presents a selective compilation of basic facts from the fields of particle entanglement and quantum information processing prepared for those non-experts in these fields that may have interest in an area of physics showing counterintuitive, ''spooky'' (Einstein's words) behavior. In fact, quantum information processing could, in the near future, provide a new technology to sustain the benefits to the U.S. economy due to advanced computer technology.
Quantum Computational Complexity of Spin Glasses
2011-03-19
canonical problem of classical statistical mechanics: computation of the classical partition function. We have approached this problem using the Potts...enumerator polynomial from coding theory and Z and exploited the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in...computational complexity of the canonical problem of classical statistical mechanics: computation of the classical partition function. We have approached this
Quantum computation with ``hot`` trapped ions
Energy Technology Data Exchange (ETDEWEB)
James, D.F.V. [Los Alamos National Lab., NM (United States); Schneider, S. [Los Alamos National Lab., NM (United States)]|[Univ. of Queensland, St. Lucia, Queensland (Australia); Milburn, G.J. [Univ. of Queensland, St. Lucia, Queensland (Australia)
1998-12-31
The authors describe two methods that have been proposed to circumvent the problem of heating by external electromagnetic fields in ion trap quantum computers. Firstly the higher order modes of ion oscillation (i.e., modes other than the center-of-mass mode) have much slower heating rates, and can therefore be employed as a reliable quantum information bus. Secondly they discuss a recently proposed method combining adiabatic passage and a number-state dependent phase shift which allows quantum gates to be performed using the center-of-mass mode as the information bus, regardless of its initial state.
Computations in quantum mechanics made easy
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
Quantum computation with ions in microscopic traps
Šašura, Marek; Steane, Andrew M.
2002-12-01
We discuss a possible experimental realization of fast quantum gates with high fidelity with ions confined in microscopic traps. The original proposal of this physical system for quantum computation comes from Cirac and Zoller (Nature 404, 579 (2000)). In this paper we analyse a sensitivity of the ion-trap quantum gate on various experimental parameters which was omitted in the original proposal. We address imprecision of laser pulses, impact of photon scattering, nonzero temperature effects and influence of laser intensity fluctuations on the total fidelity of the two-qubit phase gate.
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; YAN Hai-Yang; LI Yan-Song; TU Chang-Cun; ZHU Sheng-Jiang; RUAN Dong; SUN Yang; TAO Jia-Xun; CHEN Hao-Ming
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the "state" of anaverage particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure state densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.
Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
Knill, E
2004-01-01
The schemes for fault-tolerant postselected quantum computation given in [Knill, Fault-Tolerant Postselected Quantum Computation: Schemes, http://arxiv.org/abs/quant-ph/0402171] are analyzed to determine their error-tolerance. The analysis is based on computer-assisted heuristics. It indicates that if classical and quantum communication delays are negligible, then scalable qubit-based quantum computation is possible with errors above 1% per elementary quantum gate.
Can the human brain do quantum computing?
Rocha, A F; Massad, E; Coutinho, F A B
2004-01-01
The electrical membrane properties have been the key issues in the understanding of the cerebral physiology for more than almost two centuries. But, molecular neurobiology has now discovered that biochemical transactions play an important role in neuronal computations. Quantum computing (QC) is becoming a reality both from the theoretical point of view as well as from practical applications. Quantum mechanics is the most accurate description at atomic level and it lies behind all chemistry that provides the basis for biology ... maybe the magic of entanglement is also crucial for life. The purpose of the present paper is to discuss the dendrite spine as a quantum computing device, taking into account what is known about the physiology of the glutamate receptors and the cascade of biochemical transactions triggered by the glutamate binding to these receptors.
Quantum Computation by Adiabatic Evolution
Farhi, E; Gutmann, S; Sipser, M; Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam; Sipser, Michael
2000-01-01
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
Quantum Computing Using Superconducting Qubits
2006-04-01
highlighted in the " Molecular Motors" first feature article of the November, 2002, Physics Today, page 38. http://www.physicstoday.org/vol-5 5/iss-I I...12-2003. the article was in http://www.mosac.com/ fisica /news/leggi.php?codice= 191. News coverage in French include the following three newspapers... molecular vibra- Josephson junction devices have been proposed and experi- tional mode [12], motional quantum states of a trapped - - mentally
Methodological testing: Are fast quantum computers illusions?
Energy Technology Data Exchange (ETDEWEB)
Meyer, Steven [Tachyon Design Automation, San Francisco, CA (United States)
2013-07-01
Popularity of the idea for computers constructed from the principles of QM started with Feynman's 'Lectures On Computation', but he called the idea crazy and dependent on statistical mechanics. In 1987, Feynman published a paper in 'Quantum Implications - Essays in Honor of David Bohm' on negative probabilities which he said gave him cultural shock. The problem with imagined fast quantum computers (QC) is that speed requires both statistical behavior and truth of the mathematical formalism. The Swedish Royal Academy 2012 Nobel Prize in physics press release touted the discovery of methods to control ''individual quantum systems'', to ''measure and control very fragile quantum states'' which enables ''first steps towards building a new type of super fast computer based on quantum physics.'' A number of examples where widely accepted mathematical descriptions have turned out to be problematic are examined: Problems with the use of Oracles in P=NP computational complexity, Paul Finsler's proof of the continuum hypothesis, and Turing's Enigma code breaking versus William tutte's Colossus. I view QC research as faith in computational oracles with wished for properties. Arther Fine's interpretation in 'The Shaky Game' of Einstein's skepticism toward QM is discussed. If Einstein's reality as space-time curvature is correct, then space-time computers will be the next type of super fast computer.
Towards universal quantum computation through relativistic motion
Bruschi, David Edward; Kok, Pieter; Johansson, Göran; Delsing, Per; Fuentes, Ivette
2013-01-01
We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconducting circuits where tunable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes.
Towards Lagrangian approach to quantum computations
Vlasov, A Yu
2003-01-01
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be considered as an analogue of Weyl quantization of field theory via path integral in L. D. Faddeev's approach. Weyl quantization is possible to use also in finite-dimensional case, and some formulas may be simply rewritten with change of integrals to finite sums. On the other hand, there are specific difficulties relevant to finite case. This work has some allusions with phase space models of quantum computations developed last time by different authors.
Resource-efficient linear optical quantum computation.
Browne, Daniel E; Rudolph, Terry
2005-07-01
We introduce a scheme for linear optics quantum computation, that makes no use of teleported gates, and requires stable interferometry over only the coherence length of the photons. We achieve a much greater degree of efficiency and a simpler implementation than previous proposals. We follow the "cluster state" measurement based quantum computational approach, and show how cluster states may be efficiently generated from pairs of maximally polarization entangled photons using linear optical elements. We demonstrate the universality and usefulness of generic parity measurements, as well as introducing the use of redundant encoding of qubits to enable utilization of destructive measurements--both features of use in a more general context.
Processor core model for quantum computing.
Yung, Man-Hong; Benjamin, Simon C; Bose, Sougato
2006-06-09
We describe an architecture based on a processing "core," where multiple qubits interact perpetually, and a separate "store," where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are "always on." Alternatively, for switchable systems, our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction.
Topics in linear optical quantum computation
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
Quantum game simulator, using the circuit model of quantum computation
Vlachos, Panagiotis; Karafyllidis, Ioannis G.
2009-10-01
We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2×2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well-known quantum games, the Battle of Sexes and the Chicken game. Program summaryProgram title: Quantum Game Simulator (QGS) Catalogue identifier: AEED_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEED_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3416 No. of bytes in distributed program, including test data, etc.: 583 553 Distribution format: tar.gz Programming language: Matlab R2008a (C) Computer: Any computer that can sufficiently run Matlab R2008a Operating system: Any system that can sufficiently run Matlab R2008a Classification: 4.15 Nature of problem: Simulation of two player quantum games described by a payoff matrix. Solution method: The program calculates the matrices that comprise the Eisert setup for quantum games based on the quantum circuit model. There are 5 parameters that can be altered. We define 3 of them as constant. We play the quantum game for all possible values for the other 2 parameters and store the results in a matrix. Unusual features: The software provides an easy way of simulating any two-player quantum games. Running time: Approximately
Random Numbers and Quantum Computers
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
Quantum-Enhanced Cyber Security: Experimental Computation on Quantum-Encrypted Data
2017-03-02
AFRL-AFOSR-UK-TR-2017-0020 Quantum-Enhanced Cyber Security : Experimental Computation on Quantum-Encrypted Data Philip Walther UNIVERSITT WIEN Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Oct 2015 to 31 Dec 2016 4. TITLE AND SUBTITLE Quantum-Enhanced Cyber Security : Experimental Computation...FORM SF 298 Final Report for FA9550-1-6-1-0004 Quantum-enhanced cyber security : Experimental quantum computation with quantum-encrypted data
Quantum error correcting codes and one-way quantum computing: Towards a quantum memory
Schlingemann, D
2003-01-01
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantum computer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding and decoding operations for stabilizer codes can be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.
Quantum Computing in Non Euclidean Geometry
Resconi, Germano
2009-01-01
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics a...
A surface code quantum computer in silicon.
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.
Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious
Cirasella, Jill
2009-01-01
This article is an annotated selection of the most important and informative Internet resources for learning about quantum computing, finding quantum computing literature, and tracking quantum computing news.
Quantum computation over the butterfly network
Kinjo, Yoshiyuki; Soeda, Akihito; Turner, Peter S
2010-01-01
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 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 scenario introduced by Hayashi, which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that any controlled unitary operation can be performed without adding any entanglement resource. 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.
A simulator for quantum computer hardware
Michielsen, K.F L; de Raedt, H.A.; De Raedt, K.
2002-01-01
We present new examples of the use of the quantum computer (QC) emulator. For educational purposes we describe the implementation of the CNOT and Toffoli gate, two basic building blocks of a QC, on a three qubit NMR-like QC.
The quantum computer game: citizen science
Damgaard, Sidse; Mølmer, Klaus; Sherson, Jacob
2013-05-01
Progress in the field of quantum computation is hampered by daunting technical challenges. Here we present an alternative approach to solving these by enlisting the aid of computer players around the world. We have previously examined a quantum computation architecture involving ultracold atoms in optical lattices and strongly focused tweezers of light. In The Quantum Computer Game (see http://www.scienceathome.org/), we have encapsulated the time-dependent Schrödinger equation for the problem in a graphical user interface allowing for easy user input. Players can then search the parameter space with real-time graphical feedback in a game context with a global high-score that rewards short gate times and robustness to experimental errors. The game which is still in a demo version has so far been tried by several hundred players. Extensions of the approach to other models such as Gross-Pitaevskii and Bose-Hubbard are currently under development. The game has also been incorporated into science education at high-school and university level as an alternative method for teaching quantum mechanics. Initial quantitative evaluation results are very positive. AU Ideas Center for Community Driven Research, CODER.
Computer animations of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cohen, E. (Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique)
1992-07-01
A visualization mehtod for quantum field theories based on the transfer matrix formalism is presented. It generates computer animations simulating the time evolution of complex physical systems subject to local Hamiltonians. The method may be used as a means of gaining insight to theories such as QCD, and as an educational tool in explaining high-energy physics. (orig.).
Blind quantum computing with weak coherent pulses.
Dunjko, Vedran; Kashefi, Elham; Leverrier, Anthony
2012-05-18
The universal blind quantum computation (UBQC) protocol [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual IEEE Symposiumon Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, USA, 2009), pp. 517-526.] allows a client to perform quantum computation on a remote server. In an ideal setting, perfect privacy is guaranteed if the client is capable of producing specific, randomly chosen single qubit states. While from a theoretical point of view, this may constitute the lowest possible quantum requirement, from a pragmatic point of view, generation of such states to be sent along long distances can never be achieved perfectly. We introduce the concept of ϵ blindness for UBQC, in analogy to the concept of ϵ security developed for other cryptographic protocols, allowing us to characterize the robustness and security properties of the protocol under possible imperfections. We also present a remote blind single qubit preparation protocol with weak coherent pulses for the client to prepare, in a delegated fashion, quantum states arbitrarily close to perfect random single qubit states. This allows us to efficiently achieve ϵ-blind UBQC for any ϵ>0, even if the channel between the client and the server is arbitrarily lossy.
Geometry of abstraction in quantum computation
Pavlovic, D.; Abramsky, S.; Mislove, M.W.
2012-01-01
Quantum algorithms are sequences of abstract operations, per formed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contribu tions of Abramsky, Goecke and Selinger. In particular, we analyze f
Blind Quantum Computing with Weak Coherent Pulses
Dunjko, Vedran; Kashefi, Elham; Leverrier, Anthony
2012-05-01
The universal blind quantum computation (UBQC) protocol [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual IEEE Symposiumon Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, USA, 2009), pp. 517-526.] allows a client to perform quantum computation on a remote server. In an ideal setting, perfect privacy is guaranteed if the client is capable of producing specific, randomly chosen single qubit states. While from a theoretical point of view, this may constitute the lowest possible quantum requirement, from a pragmatic point of view, generation of such states to be sent along long distances can never be achieved perfectly. We introduce the concept of ɛ blindness for UBQC, in analogy to the concept of ɛ security developed for other cryptographic protocols, allowing us to characterize the robustness and security properties of the protocol under possible imperfections. We also present a remote blind single qubit preparation protocol with weak coherent pulses for the client to prepare, in a delegated fashion, quantum states arbitrarily close to perfect random single qubit states. This allows us to efficiently achieve ɛ-blind UBQC for any ɛ>0, even if the channel between the client and the server is arbitrarily lossy.
Simulations of Probabilities for Quantum Computing
Zak, M.
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
Quantum Computation and Information From Theory to Experiment
Imai, Hiroshi
2006-01-01
Recently, the field of quantum computation and information has been developing through a fusion of results from various research fields in theoretical and practical areas. This book consists of the reviews of selected topics charterized by great progress and cover the field from theoretical areas to experimental ones. It contains fundamental areas, quantum query complexity, quantum statistical inference, quantum cloning, quantum entanglement, additivity. It treats three types of quantum security system, quantum public key cryptography, quantum key distribution, and quantum steganography. A photonic system is highlighted for the realization of quantum information processing.
Quantum computation with nuclear spins in quantum dots
Energy Technology Data Exchange (ETDEWEB)
Christ, H.
2008-01-24
The role of nuclear spins for quantum information processing in quantum dots is theoretically investigated in this thesis. Building on the established fact that the most strongly coupled environment for the potential electron spin quantum bit are the surrounding lattice nuclear spins interacting via the hyperfine interaction, we turn this vice into a virtue by designing schemes for harnessing this strong coupling. In this perspective, the ensemble of nuclear spins can be considered an asset, suitable for an active role in quantum information processing due to its intrinsic long coherence times. We present experimentally feasible protocols for the polarization, i.e. initialization, of the nuclear spins and a quantitative solution to our derived master equation. The polarization limiting destructive interference effects, caused by the collective nature of the nuclear coupling to the electron spin, are studied in detail. Efficient ways of mitigating these constraints are presented, demonstrating that highly polarized nuclear ensembles in quantum dots are feasible. At high, but not perfect, polarization of the nuclei the evolution of an electron spin in contact with the spin bath can be efficiently studied by means of a truncation of the Hilbert space. It is shown that the electron spin can function as a mediator of universal quantum gates for collective nuclear spin qubits, yielding a promising architecture for quantum information processing. Furthermore, we show that at high polarization the hyperfine interaction of electron and nuclear spins resembles the celebrated Jaynes-Cummings model of quantum optics. This result opens the door for transfer of knowledge from the mature field of quantum computation with atoms and photons. Additionally, tailored specifically for the quantum dot environment, we propose a novel scheme for the generation of highly squeezed collective nuclear states. Finally we demonstrate that even an unprepared completely mixed nuclear spin
Quantum Computing: Theoretical versus Practical Possibility
Paraoanu, G S
2011-01-01
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle - there are no known laws of Nature that prevent it - yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I also introduce a distinction between "strong" and "weak" emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universal...
Quantum computing implementations with neutral particles
DEFF Research Database (Denmark)
Negretti, Antonio; Treutlein, Philipp; Calarco, Tommaso
2011-01-01
We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both single- and two-qubit gate implementations. We focus our discu...... optimal control theory might be a powerful tool to enhance the speed up of the gate operations as well as to achieve high fidelities required for fault tolerant quantum computation.......We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both single- and two-qubit gate implementations. We focus our...... discussion mainly on collisional quantum gates, which are best suited for atom-chip-like devices, as well as on gate proposals conceived for optical lattices. Additionally, we analyze schemes both for cold atoms confined in optical cavities and hybrid approaches to entanglement generation, and we show how...
Quantum Computers: A New Paradigm in Information Technology
Directory of Open Access Journals (Sweden)
Mahesh S. Raisinghani
2001-01-01
Full Text Available The word 'quantum' comes from the Latin word quantus meaning 'how much'. Quantum computing is a fundamentally new mode of information processing that can be performed only by harnessing physical phenomena unique to quantum mechanics (especially quantum interference. Paul Benioff of the Argonne National Laboratory first applied quantum theory to computers in 1981 and David Deutsch of Oxford proposed quantum parallel computers in 1985, years before the realization of qubits in 1995. However, it may be well into the 21st century before we see quantum computing used at a commercial level for a variety of reasons discussed in this paper. The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This paper discusses some of the current advances, applications, and chal-lenges of quantum computing as well as its impact on corporate computing and implications for management. It shows how quantum computing can be utilized to process and store information, as well as impact cryptography for perfectly secure communication, algorithmic searching, factorizing large numbers very rapidly, and simulating quantum-mechanical systems efficiently. A broad interdisciplinary effort will be needed if quantum com-puters are to fulfill their destiny as the world's fastest computing devices.
A repeat-until-success quantum computing scheme
Energy Technology Data Exchange (ETDEWEB)
Beige, A [School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom); Lim, Y L [DSO National Laboratories, 20 Science Park Drive, Singapore 118230, Singapore (Singapore); Kwek, L C [Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore (Singapore)
2007-06-15
Recently we proposed a hybrid architecture for quantum computing based on stationary and flying qubits: the repeat-until-success (RUS) quantum computing scheme. The scheme is largely implementation independent. Despite the incompleteness theorem for optical Bell-state measurements in any linear optics set-up, it allows for the implementation of a deterministic entangling gate between distant qubits. Here we review this distributed quantum computation scheme, which is ideally suited for integrated quantum computation and communication purposes.
QCWAVE, a Mathematica quantum computer simulation update
Tabakin, Frank
2011-01-01
This Mathematica 7.0/8.0 package upgrades and extends the quantum computer simulation code called QDENSITY. Use of the density matrix was emphasized in QDENSITY, although that code was also applicable to a quantum state description. In the present version, the quantum state version is stressed and made amenable to future extensions to parallel computer simulations. The add-on QCWAVE extends QDENSITY in several ways. The first way is to describe the action of one, two and three- qubit quantum gates as a set of small ($2 \\times 2, 4\\times 4$ or $8\\times 8$) matrices acting on the $2^{n_q}$ amplitudes for a system of $n_q$ qubits. This procedure was described in our parallel computer simulation QCMPI and is reviewed here. The advantage is that smaller storage demands are made, without loss of speed, and that the procedure can take advantage of message passing interface (MPI) techniques, which will hopefully be generally available in future Mathematica versions. Another extension of QDENSITY provided here is a mu...
Efficient quantum computing using coherent photon conversion.
Langford, N K; Ramelow, S; Prevedel, R; Munro, W J; Milburn, G J; Zeilinger, A
2011-10-12
Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting
Scheme for Quantum Computing Immune to Decoherence
Williams, Colin; Vatan, Farrokh
2008-01-01
A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report
Holographic computations of the Quantum Information Metric
Trivella, Andrea
2016-01-01
In this note we show how the Quantum Information Metric can be computed holographically using a perturbative approach. In particular when the deformation of the conformal field theory state is induced by a scalar operator the corresponding bulk configuration reduces to a scalar field perturbatively probing the unperturbed background. We study two concrete examples: a CFT ground state deformed by a primary operator and thermofield double state in $d=2$ deformed by a marginal operator. Finally, we generalize the bulk construction to the case of a multi dimensional parameter space and show that the Quantum Information Metric coincides with the metric of the non-linear sigma model for the corresponding scalar fields.
Ion Trap Quantum Computers: Performance Limits and Experimental Progress
Hughes, Richard
1998-03-01
In a quantum computer information would be represented by the quantum mechanical states of suitable atomic-scale systems. (A single bit of information represented by a two-level quantum system is known as a qubit.) This notion leads to the possibility of computing with quantum mechanical superpositions of numbers ("quantum parallelism"), which for certain problems would make Quantum/quantum.html>quantum computation very much more efficient than classical computation. The possibility of rapidly factoring the large integers used in public-key cryptography is an important example. (Public key cryptosystems derive their security from the difficuty of factoring, and similar problems, with conventional computers.) Quantum computational hardware development is in its infancy, but an experimental study of quantum computation with laser-cooled trapped calcium ions that is under way at Los Alamos will be described. One of the pricipal obstacles to practical quantum computation is the inevitable loss of quantum coherence of the complex quantum states involved. The results of a theoretical analysis showing that quantum factoring of small integers should be possible with trapped ions will be presented. The prospects for larger-scale computations will be discussed.
Measurement-Based and Universal Blind Quantum Computation
Broadbent, Anne; Fitzsimons, Joseph; Kashefi, Elham
Measurement-based quantum computation (MBQC) is a novel approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operation. We review here the mathematical model underlying MBQC and the first quantum cryptographic protocol designed using the unique features of MBQC.
Logic and algebraic structures in quantum computing
Eskandarian, Ali; Harizanov, Valentina S
2016-01-01
Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.
Realizing the quantum baker's map on a 3-qubit NMR quantum computer
Brun, T A; Brun, Todd A.; Schack, Ruediger
1999-01-01
By numerically simulating an implementation of the quantum baker's map on a 3-qubit NMR quantum computer based on the molecule trichloroethylene, we demonstrate the feasibility of quantum chaos experiments on present-day quantum computers. We give detailed descriptions of proposed experiments that investigate (a) the rate of entropy increase due to decoherence and (b) the phenomenon of hypersensitivity to perturbation.
QDENSITY—A Mathematica quantum computer simulation
Juliá-Díaz, Bruno; Burdis, Joseph M.; Tabakin, Frank
2009-03-01
This Mathematica 6.0 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. New version program summaryProgram title: QDENSITY 2.0 Catalogue identifier: ADXH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 26 055 No. of bytes in distributed program, including test data, etc.: 227 540 Distribution format: tar.gz Programming language: Mathematica 6.0 Operating system: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4 Catalogue identifier of previous version: ADXH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 914 Classification: 4.15 Does the new version supersede the previous version?: Offers an alternative, more up to date, implementation Nature of problem: Analysis and design of quantum circuits, quantum algorithms and quantum clusters. Solution method: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed. Reasons for new version: The package has been updated to make it fully compatible with Mathematica 6.0 Summary of revisions: The package has been updated to make it fully compatible with Mathematica 6.0 Running time: Most examples
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...
Scalable quantum computer architecture with coupled donor-quantum dot qubits
Schenkel, Thomas; Lo, Cheuk Chi; Weis, Christoph; Lyon, Stephen; Tyryshkin, Alexei; Bokor, Jeffrey
2014-08-26
A quantum bit computing architecture includes a plurality of single spin memory donor atoms embedded in a semiconductor layer, a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, wherein a first voltage applied across at least one pair of the aligned quantum dot and donor atom controls a donor-quantum dot coupling. A method of performing quantum computing in a scalable architecture quantum computing apparatus includes arranging a pattern of single spin memory donor atoms in a semiconductor layer, forming a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, applying a first voltage across at least one aligned pair of a quantum dot and donor atom to control a donor-quantum dot coupling, and applying a second voltage between one or more quantum dots to control a Heisenberg exchange J coupling between quantum dots and to cause transport of a single spin polarized electron between quantum dots.
Universal quantum gates for Single Cooper Pair Box based quantum computing
Echternach, P.; Williams, C. P.; Dultz, S. C.; Braunstein, S.; Dowling, J. P.
2000-01-01
We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.
Applications of computational quantum mechanics
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts
Non-unitary probabilistic quantum computing circuit and method
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.
How detrimental is decoherence in adiabatic quantum computation?
Albash, Tameem
2015-01-01
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit $T_2$ time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary canc...
PREFACE: Quantum Information, Communication, Computation and Cryptography
Benatti, F.; Fannes, M.; Floreanini, R.; Petritis, D.
2007-07-01
The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In view of all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12-23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy-Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two review articles, the first by G Adesso and F Illuminati discussing entanglement in continuous variable
A Geometric Algebra Perspective On Quantum Computational Gates And Universality In Quantum Computing
Cafaro, Carlo
2010-01-01
We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), we present an explicit algebraic description of one and two-qubit quantum states together with a MSTA characterization of one and two-qubit quantum computational gates. Second, using the above mentioned characterization and the GA description of the Lie algebras SO(3) and SU(2) based on the rotor group Spin+(3, 0) formalism, we reexamine Boykin's proof of universality of quantum gates. We conclude that the MSTA approach does lead to a useful conceptual unification where the complex qubit space and the complex space of unitary operators acting on them become united, with both being made just by multivectors in real space. Finally, the GA approach to rotations based on the rotor group does bring conceptual and computational advantages compared to standard vectoria...
Type II Quantum Computing Algorithm For Computational Fluid Dynamics
2006-03-01
Hall/CRC (2003) 30. Gilbert Strang, Linear Algebra and its Applications. Thompson Learning, Inc (1988) 31. George Arfken and Hans Weber, Mathematical ... method is called ensemble Figure 3. Ensemble measurement averages the measurement results of N identical quantum computers to obtain the magnitude of...the lattice Boltzmann equation. There are two methods of modeling this mesoscopic equation. The first approach is to directly simulate the
Interactive Quantum Mechanics Quantum Experiments on the Computer
Brandt, S; Dahmen, H.D
2011-01-01
Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: • harmonic waves and wave packets, • free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), • two-particle systems, coupled harmonic oscillators, • distinguishable and indistinguishable particles, • coherent and squeezed states in time-dependent motion, • quantized angular momentum, • spin and magnetic resonance, • hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...
Frahm, K M; Shepelyansky, D L; Fleckinger, Robert; Frahm, Klaus M.; Shepelyansky, Dima L.
2004-01-01
We determine the universal law for fidelity decay in quantum computations of complex dynamics in presence of internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied to quantum computations in presence of imperfections. The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chaos in the dynamical tent map with up to 18 qubits. The theory developed determines the time scales for reliable quantum computations in absence of the quantum error correction codes. These time scales are related to the Heisenberg time, the Thouless time, and the decay time given by Fermi's golden rule which are well known in the context of mesoscopic systems. The comparison is presented for static imperfection effects and random errors in quantum gates. A new convenient method for the quantum computation of the coarse-grained Wigner function is also proposed.
Software Systems for High-performance Quantum Computing
Energy Technology Data Exchange (ETDEWEB)
Humble, Travis S [ORNL; Britt, Keith A [ORNL
2016-01-01
Quantum computing promises new opportunities for solving hard computational problems, but harnessing this novelty requires breakthrough concepts in the design, operation, and application of computing systems. We define some of the challenges facing the development of quantum computing systems as well as software-based approaches that can be used to overcome these challenges. Following a brief overview of the state of the art, we present models for the quantum programming and execution models, the development of architectures for hybrid high-performance computing systems, and the realization of software stacks for quantum networking. This leads to a discussion of the role that conventional computing plays in the quantum paradigm and how some of the current challenges for exascale computing overlap with those facing quantum computing.
Applicability of Rydberg atoms to quantum computers
Ryabtsev, Igor I.; Tretyakov, Denis B.; Beterov, Ilya I.
2005-01-01
The applicability of Rydberg atoms to quantum computers is examined from an experimental point of view. In many recent theoretical proposals, the excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interactions that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analysed. We also present the results of modelling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S1/2 → 37P1/2 and two-photon 37S1/2 → 38S1/2 transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The results may be applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.
Review on the study of entanglement in quantum computation speedup
Institute of Scientific and Technical Information of China (English)
DING ShengChao; JIN Zhi
2007-01-01
The role the quantum entanglement plays in quantum computation speedup has been widely disputed.Some believe that quantum computation's speedup over classical computation is impossible if entanglement is absent, while others claim that the presence of entanglement is not a necessary condition for some quantum algorithms.This paper discusses this problem systematically.Simulating quantum computation with classical resources is analyzed and entanglement in known algorithms is reviewed.It is concluded that the presence of entanglement is a necessary but not sufficient condition in the pure state or pseudo-pure state quantum computation speedup.The case with the mixed state remains open.Further work on quantum computation will benefit from the presented results.
Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
Broadbent, Anne
2015-01-01
In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the pa...
Energy Technology Data Exchange (ETDEWEB)
Dallaire-Demers, Pierre-Luc
2016-10-07
Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counter-intuitive macroscopic phenomena such as high-temperature superconductivity. Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model. In general, no closed-form solution is known for lattices of more than one spatial dimension, but they can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists in finding its self-energy through a variational principle. As is shown in this thesis, this allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. We show theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. We also provide a gate decomposition of the cluster Hamiltonian and a simple planar architecture for a quantum simulator that can also be used to simulate more general fermionic systems. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.
Possible topological quantum computation via Khovanov homology: D-brane topological quantum computer
Vélez, Mario; Ospina, Juan
2009-05-01
A model of a D-Brane Topological Quantum Computer (DBTQC) is presented and sustained. The model is based on four-dimensional TQFTs of the Donaldson-Witten and Seiber-Witten kinds. It is argued that the DBTQC is able to compute Khovanov homology for knots, links and graphs. The DBTQC physically incorporates the mathematical process of categorification according to which the invariant polynomials for knots, links and graphs such as Jones, HOMFLY, Tutte and Bollobás-Riordan polynomials can be computed as the Euler characteristics corresponding to special homology complexes associated with knots, links and graphs. The DBTQC is conjectured as a powerful universal quantum computer in the sense that the DBTQC computes Khovanov homology which is considered like powerful that the Jones polynomial.
Milestones Toward Majorana-Based Quantum Computing
Aasen, David; Hell, Michael; Mishmash, Ryan V.; Higginbotham, Andrew; Danon, Jeroen; Leijnse, Martin; Jespersen, Thomas S.; Folk, Joshua A.; Marcus, Charles M.; Flensberg, Karsten; Alicea, Jason
2016-07-01
We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2) validation of a prototype topological qubit, and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well.
Homomorphic encryption experiments on IBM's cloud quantum computing platform
Huang, He-Liang; Zhao, You-Wei; Li, Tan; Li, Feng-Guang; Du, Yu-Tao; Fu, Xiang-Qun; Zhang, Shuo; Wang, Xiang; Bao, Wan-Su
2017-02-01
Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM's cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.
The Quantum Socket: Three-Dimensional Wiring for Extensible Quantum Computing
Béjanin, J H; Rinehart, J R; Earnest, C T; McRae, C R H; Shiri, D; Bateman, J D; Rohanizadegan, Y; Penava, B; Breul, P; Royak, S; Zapatka, M; Fowler, A G; Mariantoni, M
2016-01-01
Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum ...
Measurement-only verifiable blind quantum computing with quantum input verification
Morimae, Tomoyuki
2016-10-01
Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.
One-way quantum computing in the optical frequency comb.
Menicucci, Nicolas C; Flammia, Steven T; Pfister, Olivier
2008-09-26
One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.
Computing the Exit Complexity of Knowledge in Distributed Quantum Computers
Directory of Open Access Journals (Sweden)
M.A.Abbas
2013-01-01
Full Text Available Distributed Quantum computers abide from the exit complexity of the knowledge. The exit complexity is the accrue of the nodal information needed to clarify the total egress system with deference to a distinguished exit node. The core objective of this paper is to compile an arrogant methodology for assessing the exit complexity of the knowledge in distributed quantum computers. The proposed methodology is based on contouring the knowledge using the unlabeled binary trees, hence building an benchmarked and a computer based model. The proposed methodology dramatizes knowledge autocratically calculates the exit complexity. The methodology consists of several amphitheaters, starting with detecting the baron aspect of the tree of others entitled express knowledge and then measure the volume of information and the complexity of behavior destining from the bargain of information. Then calculate egress resulting from episodes that do not lead to the withdrawal of the information. In the end is calculated total egress complexity and then appraised total exit complexity of the system. Given the complexity of the operations within the Distributed Computing Quantity, this research addresses effective transactions that could affect the three-dimensional behavior of knowledge. The results materialized that the best affair where total exit complexity as minimal as possible is a picture of a binary tree is entitled at the rate of positive and negative cardinal points medium value. It could be argued that these cardinal points should not amass the upper bound apex or minimum.
Reversible logic synthesis methodologies with application to quantum computing
Taha, Saleem Mohammed Ridha
2016-01-01
This book opens the door to a new interesting and ambitious world of reversible and quantum computing research. It presents the state of the art required to travel around that world safely. Top world universities, companies and government institutions are in a race of developing new methodologies, algorithms and circuits on reversible logic, quantum logic, reversible and quantum computing and nano-technologies. In this book, twelve reversible logic synthesis methodologies are presented for the first time in a single literature with some new proposals. Also, the sequential reversible logic circuitries are discussed for the first time in a book. Reversible logic plays an important role in quantum computing. Any progress in the domain of reversible logic can be directly applied to quantum logic. One of the goals of this book is to show the application of reversible logic in quantum computing. A new implementation of wavelet and multiwavelet transforms using quantum computing is performed for this purpose. Rese...
The clock of a quantum computer
Apolloni, B
2002-01-01
If the physical agent (the 'pointer', or 'cursor', or 'clocking mechanism') that sequentially scans the T lines of a long computer program is a microscopic system, two quantum phenomena become relevant: spreading of the probability distribution of the pointer along the program lines, and scattering of the probability amplitude at the two endpoints of the physical space allowed for its motion. We show that the first effect determines an upper bound O(T sup - sup 2 sup / sup 3) on the probability of finding the pointer exactly at the END line. By adding an adequate number delta of further empty lines ('telomers'), one can store the result of the computation up to the moment in which the pointer is scattered back into the active region. This leads to a less severe upper bound O(sq root delta/T) on the probability of finding the pointer either at the END line or within the additional empty lines. Our analysis is performed in the context of Feynman's model of quantum computation, the only model, to our knowledge, ...
Quantum Computation: Particle and Wave Aspects of Algorithms
Patel, Apoorva
2011-01-01
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen. Clever quantum algorithms have been discovered in recent years, although not systematically, and the field remains under active investigation. Richard Feynman was one of the pioneers who foresaw the power of quantum computers. In this issue dedicated to him, I give an introduction to how particle and wave aspects contribute to the power of quantum computers. Shor's and Grover's algorithms are analysed as examples.
Quantum Computing, $NP$-complete Problems and Chaotic Dynamics
Ohya, M; Ohya, Masanori; Volovich, Igor V.
1999-01-01
An approach to the solution of NP-complete problems based on quantumcomputing and chaotic dynamics is proposed. We consider the satisfiabilityproblem and argue that the problem, in principle, can be solved in polynomialtime if we combine the quantum computer with the chaotic dynamics amplifierbased on the logistic map. We discuss a possible implementation of such achaotic quantum computation by using the atomic quantum computer with quantumgates described by the Hartree-Fock equations. In this case, in principle, onecan build not only standard linear quantum gates but also nonlinear gates andmoreover they obey to Fermi statistics. This new type of entaglement relatedwith Fermi statistics can be interesting also for quantum communication theory.
Quantum computing accelerator I/O : LDRD 52750 final report.
Energy Technology Data Exchange (ETDEWEB)
Schroeppel, Richard Crabtree; Modine, Normand Arthur; Ganti, Anand; Pierson, Lyndon George; Tigges, Christopher P.
2003-12-01
In a superposition of quantum states, a bit can be in both the states '0' and '1' at the same time. This feature of the quantum bit or qubit has no parallel in classical systems. Currently, quantum computers consisting of 4 to 7 qubits in a 'quantum computing register' have been built. Innovative algorithms suited to quantum computing are now beginning to emerge, applicable to sorting and cryptanalysis, and other applications. A framework for overcoming slightly inaccurate quantum gate interactions and for causing quantum states to survive interactions with surrounding environment is emerging, called quantum error correction. Thus there is the potential for rapid advances in this field. Although quantum information processing can be applied to secure communication links (quantum cryptography) and to crack conventional cryptosystems, the first few computing applications will likely involve a 'quantum computing accelerator' similar to a 'floating point arithmetic accelerator' interfaced to a conventional Von Neumann computer architecture. This research is to develop a roadmap for applying Sandia's capabilities to the solution of some of the problems associated with maintaining quantum information, and with getting data into and out of such a 'quantum computing accelerator'. We propose to focus this work on 'quantum I/O technologies' by applying quantum optics on semiconductor nanostructures to leverage Sandia's expertise in semiconductor microelectronic/photonic fabrication techniques, as well as its expertise in information theory, processing, and algorithms. The work will be guided by understanding of practical requirements of computing and communication architectures. This effort will incorporate ongoing collaboration between 9000, 6000 and 1000 and between junior and senior personnel. Follow-on work to fabricate and evaluate appropriate experimental nano/microstructures will be
High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
Quiroz, Gregory
2012-01-01
We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.
Lecture Script: Introduction to Computational Quantum Mechanics
Schmied, Roman
2014-01-01
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, fo...
Tomography and spectroscopy as quantum computations
Miquel, C; Saraceno, M; Knill, E H; Laflamme, R; Negrevergne, C; Miquel, Cesar; Paz, Juan Pablo; Saraceno, Marcos; Knill, Emmanuel; Laflamme, Raymond; Negrevergne, Camille
2001-01-01
Determining the state of a system and measuring properties of its evolution are two of the most important tasks a physicist faces. For the first purpose one can use tomography, a method that after subjecting the system to a number of experiments determines all independent elements of the density matrix. For the second task, one can resort to spectroscopy, a set of techniques used to determine the spectrum of eigenvalues of the evolution operator. In this letter, we show that tomography and spectroscopy can be naturally interpreted as dual forms of quantum computation. We show how to adapt the simplest case of the well-known phase estimation quantum algorithm to perform both tasks, giving it a natural interpretation as a simulated scattering experiment. We show how this algorithm can be used to implement an interesting form of tomography by performing a direct measurement of the Wigner function of a quantum system. We present results of such measurements performed on a system of three qubits using liquid state...
Radio-frequency measurement in semiconductor quantum computation
Han, TianYi; Chen, MingBo; Cao, Gang; Li, HaiOu; Xiao, Ming; Guo, GuoPing
2017-05-01
Semiconductor quantum dots have attracted wide interest for the potential realization of quantum computation. To realize efficient quantum computation, fast manipulation and the corresponding readout are necessary. In the past few decades, considerable progress of quantum manipulation has been achieved experimentally. To meet the requirements of high-speed readout, radio-frequency (RF) measurement has been developed in recent years, such as RF-QPC (radio-frequency quantum point contact) and RF-DGS (radio-frequency dispersive gate sensor). Here we specifically demonstrate the principle of the radio-frequency reflectometry, then review the development and applications of RF measurement, which provides a feasible way to achieve high-bandwidth readout in quantum coherent control and also enriches the methods to study these artificial mesoscopic quantum systems. Finally, we prospect the future usage of radio-frequency reflectometry in scaling-up of the quantum computing models.
Control aspects of quantum computing using pure and mixed states.
Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J
2012-10-13
Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.
Modular Universal Scalable Ion-trap Quantum Computer
2016-06-02
trap quantum computer . This architecture has two separate layers of scalability: the first is to increase the number of ion qubits in a single trap...Distribution Unlimited UU UU UU UU 02-06-2016 1-Aug-2010 31-Jan-2016 Final Report: Modular Universal Scalable Ion-trap Quantum Computer The views...P.O. Box 12211 Research Triangle Park, NC 27709-2211 Ion trap quantum computation , scalable modular architectures REPORT DOCUMENTATION PAGE 11
Topological quantum computing with only one mobile quasiparticle.
Simon, S H; Bonesteel, N E; Freedman, M H; Petrovic, N; Hormozi, L
2006-02-24
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2 + 1 dimensional space-time. In this Letter we show that any such quantum computation that can be done by braiding n identical quasiparticles can also be done by moving a single quasiparticle around n - 1 other identical quasiparticles whose positions remain fixed.
Modeling fluid dynamics on type II quantum computers
Scoville, James; Weeks, David; Yepez, Jeffrey
2006-03-01
A quantum algorithm is presented for modeling the time evolution of density and flow fields governed by classical equations, such as the diffusion equation, the nonlinear Burgers equation, and the damped wave equation. The algorithm is intended to run on a type-II quantum computer, a parallel quantum computer consisting of a lattice of small type I quantum computers undergoing unitary evolution and interacting via information interchanges represented by an orthogonal matrices. Information is effectively transferred between adjacent quantum computers over classical communications channels because of controlled state demolition following local quantum mechanical qubit-qubit interactions within each quantum computer. The type-II quantum algorithm presented in this paper describes a methodology for generating quantum logic operations as a generalization of classical operations associated with finite-point group symmetries. The quantum mechanical evolution of multiple qubits within each node is described. Presented is a proof that the parallel quantum system obeys a finite-difference quantum Boltzman equation at the mesoscopic scale, leading in turn to various classical linear and nonlinear effective field theories at the macroscopic scale depending on the details of the local qubit-qubit interactions.
Spin-free quantum computational simulations and symmetry adapted states
Whitfield, James Daniel
2013-01-01
The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spin-free quantum computational simulations. We go further and discuss the preparation of N-body states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. While the methods here represent adaptations of known quantum algorithms, they are the first to explicitly deal with preparing N-body symmetry-adapted states.
A quantum computer on the basis of an atomic quantum transistor with built-in quantum memory
Moiseev, S. A.; Andrianov, S. N.
2016-12-01
A quantum transistor based quantum computer where the multiqubit quantum memory is a component of the quantum transistor and, correspondingly, takes part in the performance of quantum logical operations is considered. Proceeding from the generalized Jaynes-Cummings model, equations for coefficients of the wave function of the quantum system under consideration have been obtained for different stages of its evolution in processes of performing logical operations. The solution of the system of equations allows one to establish requirements that are imposed on the parameters of the initial Hamiltonian and must be satisfied for the effective operation of the computer; it also demonstrates the possibility of a universal set of quantum operations. Thus, based on the proposed approach, the possibility of constructing a compact multiatomic ensemble based on quantum computer using a quantum transistor for the implementation of two-qubit gates has been demonstrated.
Quantum Annealing and Computation: A Brief Documentary Note
Ghosh, Asim
2013-01-01
Major breakthrough in quantum computation has recently been achieved using quantum annealing to develop analog quantum computers instead of gate based computers. After a short introduction to quantum computation, we retrace very briefly the history of these developments and discuss the Indian researches in this connection and provide some interesting documents (in the Figs.) obtained from a chosen set of high impact papers (and also some recent news etc. blogs appearing in the Internet). This note is also designed to supplement an earlier note by Bose (Science and Culture, 79, pp. 337-378, 2013).
Baianu,I C
2004-01-01
The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In previous publications (Baianu,1971a, b) the formal concept of quantum automaton and quantum computation, respectively, were introduced and their possible implications for genetic processes and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b; 1977; 1987; 2004; Baianu et al, 2004). The notions of topological semigroup, quantum automaton, or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebra...
Classical and quantum computing with C++ and Java simulations
Hardy, Y
2001-01-01
Classical and Quantum computing provides a self-contained, systematic and comprehensive introduction to all the subjects and techniques important in scientific computing. The style and presentation are readily accessible to undergraduates and graduates. A large number of examples, accompanied by complete C++ and Java code wherever possible, cover every topic. Features and benefits: - Comprehensive coverage of the theory with many examples - Topics in classical computing include boolean algebra, gates, circuits, latches, error detection and correction, neural networks, Turing machines, cryptography, genetic algorithms - For the first time, genetic expression programming is presented in a textbook - Topics in quantum computing include mathematical foundations, quantum algorithms, quantum information theory, hardware used in quantum computing This book serves as a textbook for courses in scientific computing and is also very suitable for self-study. Students, professionals and practitioners in computer...
A Blueprint for a Topologically Fault-tolerant Quantum Computer
Bonderson, Parsa; Freedman, Michael; Nayak, Chetan
2010-01-01
The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical" computer, including any potential non-quantum technologies the future may bring. However, the fragility of quantum states poses a challenging obstacle for realization of a fault-tolerant quantum computer. The topological approach to quantum computation proposes to surmount this obstacle by using special physical systems -- non-Abelian topologically ordered phases of matter -- that would provide intrinsic fault-tolerance at the hardware level. The so-called "Ising-type" non-Abelian topological order is likely to be physically realized in a number of systems, but it can only provide a universal gate set (a requisite for quantum computation) if one has the ability to perform certain dynamical topology-changing operations on the system. Until now, practical methods of implementing thes...
Computer science approach to quantum control
Energy Technology Data Exchange (ETDEWEB)
Janzing, D.
2006-07-01
Whereas it is obvious that every computation process is a physical process it has hardly been recognized that many complex physical processes bear similarities to computation processes. This is in particular true for the control of physical systems on the nanoscopic level: usually the system can only be accessed via a rather limited set of elementary control operations and for many purposes only a concatenation of a large number of these basic operations will implement the desired process. This concatenation is in many cases quite similar to building complex programs from elementary steps and principles for designing algorithm may thus be a paradigm for designing control processes. For instance, one can decrease the temperature of one part of a molecule by transferring its heat to the remaining part where it is then dissipated to the environment. But the implementation of such a process involves a complex sequence of electromagnetic pulses. This work considers several hypothetical control processes on the nanoscopic level and show their analogy to computation processes. We show that measuring certain types of quantum observables is such a complex task that every instrument that is able to perform it would necessarily be an extremely powerful computer. Likewise, the implementation of a heat engine on the nanoscale requires to process the heat in a way that is similar to information processing and it can be shown that heat engines with maximal efficiency would be powerful computers, too. In the same way as problems in computer science can be classified by complexity classes we can also classify control problems according to their complexity. Moreover, we directly relate these complexity classes for control problems to the classes in computer science. Unifying notions of complexity in computer science and physics has therefore two aspects: on the one hand, computer science methods help to analyze the complexity of physical processes. On the other hand, reasonable
Simply Explain the computation Ability of Quantum Computation%浅释量子计算的计算能力
Institute of Scientific and Technical Information of China (English)
匡春光
2001-01-01
Quantum computation is a new field of computer science. It is given attention to for its powerful computation ability. The paper explains the cause of its powerful computation ability by giving two typical quantum computation algorithms.
Preparing projected entangled pair states on a quantum computer.
Schwarz, Martin; Temme, Kristan; Verstraete, Frank
2012-03-16
We present a quantum algorithm to prepare injective projected entangled pair states (PEPS) on a quantum computer, a class of open tensor networks representing quantum states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.
Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation
Directory of Open Access Journals (Sweden)
Qiao Bi
2010-01-01
Full Text Available A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the subspaces are just projected states which are ruled by a subdynamic kinetic equation. These projected states can be used to perform ideal quantum logical operations without decoherence.
Consequences and Limitations of Conventional Computers and their Solutions through Quantum Computers
Directory of Open Access Journals (Sweden)
Nilesh BARDE
2012-08-01
Full Text Available Quantum computer is the current topic of research in the field of computational science, which uses principles of quantum mechanics. Quantum computers will be much more powerful than the classical computer due to its enormous computational speed. Recent developments in quantum computers which are based on the laws of quantum mechanics, shows different ways of performing efficient calculations along with the various results which are not possible on the classical computers in an efficient period of time. One of the most striking results that have obtained on the quantum computers is the prime factorization of the large integer in a polynomial time. The idea of involvement of the quantum mechanics for the computational purpose is outlined briefly in the present work that reflects the importance and advantages of the next generation of the 21st century classical computers, named as quantum computers, in terms of the cost as well as time period required for the computation purpose. Present paper presents a quantum computer simulator for executing the limitations of classical computer with respect to time and the number of digits of a composite integer used for calculating its prime factors.
D'Ariano, Giacomo Mauro
2010-01-01
I argue that the program on operational foundations of Quantum Mechanics 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 proposed operational "principles of the quantumness", I address the problem on whether Quantum Mechanics and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from Quantum Mechanics, within the computational paradigm "the universe is a huge quantum computer", reformulating QFT as a Quantum-Circuit Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance, and even the quantization rule and the Plank constant, which resort to being properties of the underlying causal tapestry of space-time. In this w...
Blueprint for a microwave trapped ion quantum computer.
Lekitsch, Bjoern; Weidt, Sebastian; Fowler, Austin G; Mølmer, Klaus; Devitt, Simon J; Wunderlich, Christof; Hensinger, Winfried K
2017-02-01
The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion-based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation-based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error-threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects.
Blueprint for a microwave trapped ion quantum computer
Lekitsch, Bjoern; Weidt, Sebastian; Fowler, Austin G.; Mølmer, Klaus; Devitt, Simon J.; Wunderlich, Christof; Hensinger, Winfried K.
2017-01-01
The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion–based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation–based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error–threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects. PMID:28164154
The computer-based model of quantum measurements
Sevastianov, L. A.; Zorin, A. V.
2017-07-01
Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic systems are rarely taken into account in computing algorithms and calculations. In the previous studies of the authors, constructive model of quantum measurements has been developed and implemented in the form of symbolic and numerical calculations for the hydrogen-like atoms. This work describes a generalization of these results to the alkali metal atoms.
QCMPI: A parallel environment for quantum computing
Tabakin, Frank; Juliá-Díaz, Bruno
2009-06-01
QCMPI is a quantum computer (QC) simulation package written in Fortran 90 with parallel processing capabilities. It is an accessible research tool that permits rapid evaluation of quantum algorithms for a large number of qubits and for various "noise" scenarios. The prime motivation for developing QCMPI is to facilitate numerical examination of not only how QC algorithms work, but also to include noise, decoherence, and attenuation effects and to evaluate the efficacy of error correction schemes. The present work builds on an earlier Mathematica code QDENSITY, which is mainly a pedagogic tool. In that earlier work, although the density matrix formulation was featured, the description using state vectors was also provided. In QCMPI, the stress is on state vectors, in order to employ a large number of qubits. The parallel processing feature is implemented by using the Message-Passing Interface (MPI) protocol. A description of how to spread the wave function components over many processors is provided, along with how to efficiently describe the action of general one- and two-qubit operators on these state vectors. These operators include the standard Pauli, Hadamard, CNOT and CPHASE gates and also Quantum Fourier transformation. These operators make up the actions needed in QC. Codes for Grover's search and Shor's factoring algorithms are provided as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to alternate noise effects, which corresponds to the idea of solving a stochastic Schrödinger equation. The density matrix for the ensemble of such noise cases is constructed using parallel distribution methods to evaluate its eigenvalues and associated entropy. Potential applications of this powerful tool include studies of the stability and correction of QC processes using Hamiltonian based dynamics. Program summaryProgram title: QCMPI Catalogue identifier: AECS_v1_0 Program summary URL
Practical experimental certification of computational quantum gates via twirling
Moussa, Osama; Ryan, Colm A; Laflamme, Raymond
2011-01-01
Due to the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the computation process via quantum process tomography requires an exponential amount of resources, and thus is not practical even for relatively small devices. We solve this problem by demonstrating that twirling experiments previously used to characterize the average fidelity of quantum memories efficiently can be easily adapted to estimate the average fidelity of the experimental implementation of important quantum computation processes, such as unitaries in the Clifford group, in a practical and efficient manner with applicability in current quantum devices. Using this procedure, we demonstrate state-of-the-art coherent control of an ensemble of magnetic moments of nuclear spins in a single crystal solid by implementing the encoding operation for a 3 qubit code with only a 1% degrada...
From transistor to trapped-ion computers for quantum chemistry.
Yung, M-H; Casanova, J; Mezzacapo, A; McClean, J; Lamata, L; Aspuru-Guzik, A; Solano, E
2014-01-07
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.
Blueprint for a microwave trapped-ion quantum computer
DEFF Research Database (Denmark)
Lekitsch, B.; Weidt, S.; Fowler, A. G.
2017-01-01
constructed using a modular approach. We present a blueprint for a trapped-ion based scalable quantum computer module which makes it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units......, are constructed using silicon microfabrication techniques and they are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength-radiation based quantum gate technology. To scale this microwave quantum computer architecture to an arbitrary size we...... present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high-error-threshold surface error correction code can be implemented in the proposed architecture to execute fault...
Experimental Blind Quantum Computing for a Classical Client
Huang, He-Liang; Zhao, Qi; Ma, Xiongfeng; Liu, Chang; Su, Zu-En; Wang, Xi-Lin; Li, Li; Liu, Nai-Le; Sanders, Barry C.; Lu, Chao-Yang; Pan, Jian-Wei
2017-08-01
To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.
Milestones Toward Majorana-Based Quantum Computing
Directory of Open Access Journals (Sweden)
David Aasen
2016-08-01
Full Text Available We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1 detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2 validation of a prototype topological qubit, and (3 demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system’s excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well.
Quantum Computing in Fock Space Systems
Berezin, Alexander A.
1997-04-01
Fock space system (FSS) has unfixed number (N) of particles and/or degrees of freedom. In quantum computing (QC) main requirement is sustainability of coherent Q-superpositions. This normally favoured by low noise environment. High excitation/high temperature (T) limit is hence discarded as unfeasible for QC. Conversely, if N is itself a quantized variable, the dimensionality of Hilbert basis for qubits may increase faster (say, N-exponentially) than thermal noise (likely, in powers of N and T). Hence coherency may win over T-randomization. For this type of QC speed (S) of factorization of long integers (with D digits) may increase with D (for 'ordinary' QC speed polynomially decreases with D). This (apparent) paradox rests on non-monotonic bijectivity (cf. Georg Cantor's diagonal counting of rational numbers). This brings entire aleph-null structurality ("Babylonian Library" of infinite informational content of integer field) to superposition determining state of quantum analogue of Turing machine head. Structure of integer infinititude (e.g. distribution of primes) results in direct "Platonic pressure" resembling semi-virtual Casimir efect (presure of cut-off vibrational modes). This "effect", the embodiment of Pythagorean "Number is everything", renders Godelian barrier arbitrary thin and hence FSS-based QC can in principle be unlimitedly efficient (e.g. D/S may tend to zero when D tends to infinity).
Progress in silicon-based quantum computing.
Clark, R G; Brenner, R; Buehler, T M; Chan, V; Curson, N J; Dzurak, A S; Gauja, E; Goan, H S; Greentree, A D; Hallam, T; Hamilton, A R; Hollenberg, L C L; Jamieson, D N; McCallum, J C; Milburn, G J; O'Brien, J L; Oberbeck, L; Pakes, C I; Prawer, S D; Reilly, D J; Ruess, F J; Schofield, S R; Simmons, M Y; Stanley, F E; Starrett, R P; Wellard, C; Yang, C
2003-07-15
We review progress at the Australian Centre for Quantum Computer Technology towards the fabrication and demonstration of spin qubits and charge qubits based on phosphorus donor atoms embedded in intrinsic silicon. Fabrication is being pursued via two complementary pathways: a 'top-down' approach for near-term production of few-qubit demonstration devices and a 'bottom-up' approach for large-scale qubit arrays with sub-nanometre precision. The 'top-down' approach employs a low-energy (keV) ion beam to implant the phosphorus atoms. Single-atom control during implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure. In contrast, the 'bottom-up' approach uses scanning tunnelling microscope lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. In both cases, surface electrodes control the qubit using voltage pulses, and dual single-electron transistors operating near the quantum limit provide fast read-out with spurious-signal rejection.
A quantum computer based on recombination processes in microelectronic devices
Theodoropoulos, K.; Ntalaperas, D.; Petras, I.; Konofaos, N.
2005-01-01
In this paper a quantum computer based on the recombination processes happening in semiconductor devices is presented. A "data element" and a "computational element" are derived based on Schokley-Read-Hall statistics and they can later be used to manifest a simple and known quantum computing process. Such a paradigm is shown by the application of the proposed computer onto a well known physical system involving traps in semiconductor devices.
A quantum computer based on recombination processes in microelectronic devices
Energy Technology Data Exchange (ETDEWEB)
Theodoropoulos, K [Computer Engineering and Informatics Department, University of Patras, Patras (Greece); Ntalaperas, D [Computer Engineering and Informatics Department, University of Patras, Patras (Greece); Research Academic Computer Technology Institute, Riga Feraiou 61, 26110, Patras (Greece); Petras, I [Computer Engineering and Informatics Department, University of Patras, Patras (Greece); Konofaos, N [Computer Engineering and Informatics Department, University of Patras, Patras (Greece)
2005-01-01
In this paper a quantum computer based on the recombination processes happening in semiconductor devices is presented. A 'data element' and a 'computational element' are derived based on Schokley-Read-Hall statistics and they can later be used to manifest a simple and known quantum computing process. Such a paradigm is shown by the application of the proposed computer onto a well known physical system involving traps in semiconductor devices.
The Brain Is both Neurocomputer and Quantum Computer
Hameroff, Stuart R.
2007-01-01
In their article, "Is the Brain a Quantum Computer,?" Litt, Eliasmith, Kroon, Weinstein, and Thagard (2006) criticize the Penrose-Hameroff "Orch OR" quantum computational model of consciousness, arguing instead for neurocomputation as an explanation for mental phenomena. Here I clarify and defend Orch OR, show how Orch OR and neurocomputation are…
Demonstration of a small programmable quantum computer with atomic qubits.
Debnath, S; Linke, N M; Figgatt, C; Landsman, K A; Wright, K; Monroe, C
2016-08-04
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
Fundamentals of universality in one-way quantum computation
Van den Nest, M; Dür, W; Miyake, A
2007-01-01
We build a framework allowing for a systematic investigation of the issue: "Which quantum states are universal resources for one-way quantum computation?" We start by re-examining what is exactly meant by "universality" in quantum computation, and what the implications are for universal one-way quantum computation. Given the framework of a measurement-based quantum computer, where quantum information is processed by local operations only, the most general universal one-way quantum computer is one which is capable of accepting arbitrary classical inputs and producing arbitrary quantum outputs--we refer to this property as CQ-universality. We then show that a systematic study of CQ-universality in one-way quantum computation is possible by identifying entanglement features that must be present in every universal resource. These insights are used to identify several states as being not universal, such as 1D cluster states, W states, and ground states of non-critical 1D spin systems. Our criteria are strengthened...
Demonstration of a small programmable quantum computer with atomic qubits
Debnath, S.; Linke, N. M.; Figgatt, C.; Landsman, K. A.; Wright, K.; Monroe, C.
2016-08-01
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
Lau, Hoi-Kwan; Plenio, Martin B.
2016-09-01
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.
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding.
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.
Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
Broadbent, Anne
2016-08-01
In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the parties share nonlocal correlations as given by the Popescu-Rohrlich box. This means that communication is not required for efficient instantaneous nonlocal quantum computation. Exploiting the well-known relation to position-based cryptography, our result also implies the impossibility of secure position-based cryptography against adversaries with nonsignaling correlations. Furthermore, our construction establishes a quantum analog of the classical communication complexity collapse under nonsignaling correlations.
Cluster State Quantum Computation and the Repeat-Until Scheme
Kwek, L. C.
Cluster state computation or the one way quantum computation (1WQC) relies on an initially highly entangled state (called a cluster state) and an appropriate sequence of single qubit measurements along different directions, together with feed-forward based on the measurement results, to realize a quantum computation process. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis. In this short tutorial on cluster state quantum computation, we will also describe the basic ideas of a cluster state and proceed to describe how a single qubit operation can be done on a cluster state. Recently, we proposed a repeat-until-success (RUS) scheme that could effectively be used to realize one-way quantum computer on a hybrid system of photons and atoms. We will briefly describe this RUS scheme and show how it can be used to entangled two distant stationary qubits.
Dorit Aharonov; Umesh Vazirani
2012-01-01
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Quantum Cryptography, Quantum Communication, and Quantum Computer in a Noisy Environment
Nagata, Koji; Nakamura, Tadao
2017-07-01
First, we study several information theories based on quantum computing in a desirable noiseless situation. (1) We present quantum key distribution based on Deutsch's algorithm using an entangled state. (2) We discuss the fact that the Bernstein-Vazirani algorithm can be used for quantum communication including an error correction. Finally, we discuss the main result. We study the Bernstein-Vazirani algorithm in a noisy environment. The original algorithm determines a noiseless function. Here we consider the case that the function has an environmental noise. We introduce a noise term into the function f( x). So we have another noisy function g( x). The relation between them is g( x) = f( x) ± O( 𝜖). Here O( 𝜖) ≪ 1 is the noise term. The goal is to determine the noisy function g( x) with a success probability. The algorithm overcomes classical counterpart by a factor of N in a noisy environment.
Experimental magic state distillation for fault-tolerant quantum computing.
Souza, Alexandre M; Zhang, Jingfu; Ryan, Colm A; Laflamme, Raymond
2011-01-25
Any physical quantum device for quantum information processing (QIP) is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error-correcting or error-avoiding methods. Fault-tolerance achieved through quantum error correction will be an integral part of quantum computers. Of the many methods that have been discovered to implement it, a highly successful approach has been to use transversal gates and specific initial states. A critical element for its implementation is the availability of high-fidelity initial states, such as |0〉 and the 'magic state'. Here, we report an experiment, performed in a nuclear magnetic resonance (NMR) quantum processor, showing sufficient quantum control to improve the fidelity of imperfect initial magic states by distilling five of them into one with higher fidelity.
Experimental magic state distillation for fault-tolerant quantum computing
Souza, Alexandre M; Ryan, Colm A; Laflamme, Raymond; 10.1038/ncomms1166
2011-01-01
Any physical quantum device for quantum information processing is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error correcting or error avoiding methods. Fault-tolerance achieved through quantum error correction will be an integral part of quantum computers. Of the many methods that have been discovered to implement it, a highly successful approach has been to use transversal gates and specific initial states. A critical element for its implementation is the availability of high-fidelity initial states such as |0> and the Magic State. Here we report an experiment, performed in a nuclear magnetic resonance (NMR) quantum processor, showing sufficient quantum control to improve the fidelity of imperfect initial magic states by distilling five of them into one with higher fidelity.
The 2004 Latsis Symposium: Quantum optics for Communication and Computing
2004-01-01
1-3 March 2004 Ecole Polytechnique Fédérale de Lausanne Auditoire SG1 The field of Quantum Optics covers topics that extend from basic physical concepts, regarding the quantum description of light, matter, and light-matter interaction, to the applications of these concepts in future information and communication technologies. This field is of primary importance for science and society for two reasons. Firstly, it brings a deeper physical understanding of the fundamental aspects of modern quantum physics. Secondly, it offers perspectives for the invention and implementation of new devices and systems in the fields of communications, information management and computing. The themes that will be addressed in the Latsis Symposium on Quantum Optics are quantum communications, quantum computation, and quantum photonic devices. The objective of the symposium is to give an overview of this fascinating and rapidly evolving field. The different talks will establish links between new fundamental c...
The 2004 Latsis Symposium: Quantum optics for Communication and Computing
2004-01-01
1-3 March 2004 Ecole Polytechnique Fédérale de Lausanne Auditoire SG1 The field of Quantum Optics covers topics that extend from basic physical concepts, regarding the quantum description of light, matter, and light-matter interaction, to the applications of these concepts in future information and communication technologies. This field is of primary importance for science and society for two reasons. Firstly, it brings a deeper physical understanding of the fundamental aspects of modern quantum physics. Secondly, it offers perspectives for the invention and implementation of new devices and systems in the fields of communications, information management and computing. The themes that will be addressed in the Latsis Symposium on Quantum Optics are quantum communications, quantum computation, and quantum photonic devices. The objective of the symposium is to give an overview of this fascinating and rapidly evolving field. The different talks will establish links between new fundamental ...
The 2004 Latsis Symposium: Quantum optics for Communication and Computing
2004-01-01
1-3 March 2004 Ecole Polytechnique Fédérale de Lausanne Auditoire SG1 The field of Quantum Optics covers topics that extend from basic physical concepts, regarding the quantum description of light, matter, and light-matter interaction, to the applications of these concepts in future information and communication technologies. This field is of primary importance for science and society for two reasons. Firstly, it brings a deeper physical understanding of the fundamental aspects of modern quantum physics. Secondly, it offers perspectives for the invention and implementation of new devices and systems in the fields of communications, information management and computing. The themes that will be addressed in the Latsis Symposium on Quantum Optics are quantum communications, quantum computation, and quantum photonic devices. The objective of the symposium is to give an overview of this fascinating and rapidly evolving field. The different talks will establish links between new fundamental...
High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation
Yang, W L; Hu, Y; Feng, M; Du, J F
2011-01-01
We study a hybrid quantum computing system using nitrogen-vacancy center ensemble (NVE) as quantum memory, current-biased Josephson junction (CBJJ) superconducting qubit fabricated in a transmission line resonator (TLR) as quantum computing processor and the microwave photons in TLR as quantum data bus. The storage process is seriously treated by considering all kinds of decoherence mechanisms. Such a hybrid quantum device can also be used to create multi-qubit W states of NVEs through a common CBJJ. The experimental feasibility and challenge are justified using currently available technology.
Continuous-variable quantum computing in optical time-frequency modes using quantum memories.
Humphreys, Peter C; Kolthammer, W Steven; Nunn, Joshua; Barbieri, Marco; Datta, Animesh; Walmsley, Ian A
2014-09-26
We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that are a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.
Moll, Nikolaj; Fuhrer, Andreas; Staar, Peter; Tavernelli, Ivano
2016-07-01
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.
Quantum computation in a quantum-dot-Majorana-fermion hybrid system
Xue, Zheng-Yuan
2012-01-01
We propose a scheme to implement universal quantum computation in a quantum-dot-Majorana-fermion hybrid system. Quantum information is encoded on pairs of Majorana fermions, which live on the the interface between topologically trivial and nontrivial sections of a quantum nanowire deposited on an s-wave superconductor. Universal single-qubit gates on topological qubit can be achieved. A measurement-based two-qubit Controlled-Not gate is produced with the help of parity measurements assisted by the quantum-dot and followed by prescribed single-qubit gates. The parity measurement, on the quantum-dot and a topological qubit, is achieved by the Aharonov- Casher effect.
Quantum Monte Carlo Endstation for Petascale Computing
Energy Technology Data Exchange (ETDEWEB)
Lubos Mitas
2011-01-26
NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13
Statistical Mechanics of Classical and Quantum Computational Complexity
Laumann, C. R.; Moessner, R.; Scardicchio, A.; Sondhi, S. L.
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous framework for classifying the hardness of problems according to the computational resources, most notably time, needed to solve them. Its extension to quantum computers allows the relative power of quantum computers to be analyzed. This framework identifies families of problems which are likely hard for classical computers ("NP-complete") and those which are likely hard for quantum computers ("QMA-complete") by indirect methods. That is, they identify problems of comparable worst-case difficulty without directly determining the individual hardness of any given instance. Statistical mechanical methods can be used to complement this classification by directly extracting information about particular families of instances—typically those that involve optimization—by studying random ensembles of them. These pose unusual and interesting (quantum) statistical mechanical questions and the results shed light on the difficulty of problems for large classes of algorithms as well as providing a window on the contrast between typical and worst case complexity. In these lecture notes we present an introduction to this set of ideas with older work on classical satisfiability and recent work on quantum satisfiability as primary examples. We also touch on the connection of computational hardness with the physical notion of glassiness.
Quantum simulation of a three-body interaction Hamiltonian on an NMR quantum computer
Tseng, C H; Sharf, Y; Knill, E H; Laflamme, R; Havel, T F; Cory, D G
2000-01-01
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on 13-C labelled Alanine by creating the non-physical Hamiltonian ZZZ corresponding to a three body interaction.
Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer
Energy Technology Data Exchange (ETDEWEB)
Tseng, C. H. [Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Somaroo, S. [Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Sharf, Y. [Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Knill, E. [Theoretical Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87455 (United States); Laflamme, R. [Theoretical Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87455 (United States); Havel, T. F. [BCMP Harvard Medical School, 240 Longwood Avenue, Boston Massachusetts 02115 (United States); Cory, D. G. [Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2000-01-01
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on {sup 13}C labeled alanine by creating the nonphysical Hamiltonian {sigma}{sub z}{sigma}{sub z}{sigma}{sub z} corresponding to a three-body interaction. (c) 1999 The American Physical Society.
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-09
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Digitized adiabatic quantum computing with a superconducting circuit
Barends, R.; Shabani, A.; Lamata, L.; Kelly, J.; Mezzacapo, A.; Heras, U. Las; Babbush, R.; Fowler, A. G.; Campbell, B.; Chen, Yu; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; O'Malley, P. J. J.; Quintana, C.; Roushan, P.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Solano, E.; Neven, H.; Martinis, John M.
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Quantum computing with acceptor spins in silicon.
Salfi, Joe; Tong, Mengyang; Rogge, Sven; Culcer, Dimitrie
2016-06-17
The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time [Formula: see text] as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.
Statistical constraints on state preparation for a quantum computer
Indian Academy of Sciences (India)
Subhash Kak
2001-10-01
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. We show that the constraints of quantum statistics require that the entropy of the system be brought down when several independent qubits are assembled together. In particular, we have: (i) not all initial states are realizable as pure states; (ii) the temperature of the system must be reduced. These factors, in addition to decoherence and sensitivity to errors, must be considered in the implementation of quantum computers.
On Computational Power of Quantum Read-Once Branching Programs
Directory of Open Access Journals (Sweden)
Farid Ablayev
2011-03-01
Full Text Available In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting technique, we show that any Boolean function with linear polynomial presentation can be computed by a quantum read-once branching program using a relatively small (usually logarithmic in the size of input number of qubits. Then we show that the described class of Boolean functions is closed under the polynomial projections.
Symbolic Quantum Computation Simulation in SymPy
Cugini, Addison; Curry, Matt; Granger, Brian
2010-10-01
Quantum computing is an emerging field which aims to use quantum mechanics to solve difficult computational problems with greater efficiency than on a classical computer. There is a need to create software that i) helps newcomers to learn the field, ii) enables practitioners to design and simulate quantum circuits and iii) provides an open foundation for further research in the field. Towards these ends we have created a package, in the open-source symbolic computation library SymPy, that simulates the quantum circuit model of quantum computation using Dirac notation. This framework builds on the extant powerful symbolic capabilities of SymPy to preform its simulations in a fully symbolic manner. We use object oriented design to abstract circuits as ordered collections of quantum gate and qbit objects. The gate objects can either be applied directly to the qbit objects or be represented as matrices in different bases. The package is also capable of performing the quantum Fourier transform and Shor's algorithm. A notion of measurement is made possible through the use of a non-commutative gate object. In this talk, we describe the software and show examples of quantum circuits on single and multi qbit states that involve common algorithms, gates and measurements.
Quantum computing and prospects of quantum computers%量子计算与量子计算机展望
Institute of Scientific and Technical Information of China (English)
林雄; 林帅
2012-01-01
量子计算和量子计算机的研究是当代信息科学所面临的一个重大科学课题。阐述了量子计算、量子逻辑门的基本概念和Shor算法，指出了当前实现大规模量子计算所遇到的困难和可能的解决办法。%The study of quantum computing and quantum computers is a major scientific subject of contemporary information science research. This article gives an introduction to quantum computing, describes the basic concepts of quantum logic gates and Shor's algorithm, points out the difficulties encountered in the current large-scale quantum computing and possible solutions.
State of the art and prospects for quantum computing
Dyakonov, M I
2012-01-01
This is a brief review of the experimental and theoretical quantum computing. The hopes for eventually building a useful quantum computer rely entirely on the so-called "threshold theorem". In turn, this theorem is based on a number of assumptions, treated as axioms, i.e. as being satisfied exactly. Since in reality this is not possible, the prospects of scalable quantum computing will remain uncertain until the required precision, with which these assumptions should be approached, is established. Some related sociological aspects are also discussed. .
Fully fault tolerant quantum computation with non-deterministic gates
Li, Ying; Stace, Thomas M; Benjamin, Simon C
2010-01-01
In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should assumed to be failure prone. In the logical limit of this architecture each component contains only one qubit. Here we derive thresholds for fault tolerant quantum computation under such extreme paradigms. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded, meanwhile the rate of unknown errors should not exceed 2 in 10^4 operations.
Entanglement and deterministic quantum computing with one qubit
Boyer, Michel; Brodutch, Aharon; Mor, Tal
2017-02-01
The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present tools for learning about entanglement and quantum correlations in dynamical systems where the quantum states are mixed and the eigenvalue spectrum is highly degenerate. We apply these results to the deterministic quantum computing with one qubit (DQC1) computation model and show that the states generated in a DQC1 circuit have an eigenvalue structure that makes them difficult to entangle, even when they are relatively far from the completely mixed state. Our results strengthen the conjecture that it may be possible to find quantum algorithms that do not generate entanglement and yet still have an exponential advantage over their classical counterparts.
Cryogenic setup for trapped ion quantum computing.
Brandl, M F; van Mourik, M W; Postler, L; Nolf, A; Lakhmanskiy, K; Paiva, R R; Möller, S; Daniilidis, N; Häffner, H; Kaushal, V; Ruster, T; Warschburger, C; Kaufmann, H; Poschinger, U G; Schmidt-Kaler, F; Schindler, P; Monz, T; Blatt, R
2016-11-01
We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120 dB reduction of 50 Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than ±20 nm over 2 s. In addition to the cryogenic apparatus, we describe the setup required for an operation with (40)Ca(+) and (88)Sr(+) ions. The instability of the laser manipulating the optical qubits in (40)Ca(+) is characterized by yielding a minimum of its Allan deviation of 2.4 ⋅ 10(-15) at 0.33 s. To evaluate the performance of the apparatus, we trapped (40)Ca(+) ions, obtaining a heating rate of 2.14(16) phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8) ms.
General approaches in ensemble quantum computing
Indian Academy of Sciences (India)
V Vimalan; N Chandrakumar
2008-01-01
We have developed methodology for NMR quantum computing focusing on enhancing the efficiency of initialization, of logic gate implementation and of readout. Our general strategy involves the application of rotating frame pulse sequences to prepare pseudopure states and to perform logic operations. We demonstrate experimentally our methodology for both homonuclear and heteronuclear spin ensembles. On model two-spin systems, the initialization time of one of our sequences is three-fourths (in the heteronuclear case) or one-fourth (in the homonuclear case), of the typical pulsed free precession sequences, attaining the same initialization efficiency. We have implemented the logical SWAP operation in homonuclear AMX spin systems using selective isotropic mixing, reducing the duration taken to a third compared to the standard re-focused INEPT-type sequence. We introduce the 1D version for readout of the rotating frame SWAP operation, in an attempt to reduce readout time. We further demonstrate the Hadamard mode of 1D SWAP, which offers 2N-fold reduction in experiment time for a system with -working bits, attaining the same sensitivity as the standard 1D version.
Cryogenic setup for trapped ion quantum computing
Brandl, M. F.; van Mourik, M. W.; Postler, L.; Nolf, A.; Lakhmanskiy, K.; Paiva, R. R.; Möller, S.; Daniilidis, N.; Häffner, H.; Kaushal, V.; Ruster, T.; Warschburger, C.; Kaufmann, H.; Poschinger, U. G.; Schmidt-Kaler, F.; Schindler, P.; Monz, T.; Blatt, R.
2016-11-01
We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120 dB reduction of 50 Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than ±20 nm over 2 s. In addition to the cryogenic apparatus, we describe the setup required for an operation with 40Ca+ and 88Sr+ ions. The instability of the laser manipulating the optical qubits in 40Ca+ is characterized by yielding a minimum of its Allan deviation of 2.4 ṡ 10-15 at 0.33 s. To evaluate the performance of the apparatus, we trapped 40Ca+ ions, obtaining a heating rate of 2.14(16) phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8) ms.
Cryogenic setup for trapped ion quantum computing
Brandl, M F; Postler, L; Nolf, A; Lakhmanskiy, K; Paiva, R R; Möller, S; Daniilidis, N; Häffner, H; Kaushal, V; Ruster, T; Warschburger, C; Kaufmann, H; Poschinger, U G; Schmidt-Kaler, F; Schindler, P; Monz, T; Blatt, R
2016-01-01
We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120~dB reduction of 50~Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than $\\pm$20~nm over 2~s. In addition to the cryogenic apparatus, we describe the setup required for an operation with $^{\\mathrm{40}}$Ca$^{\\mathrm{+}}$ and $^{\\mathrm{88}}$Sr$^{\\mathrm{+}}$ ions. The instability of the laser manipulating the optical qubits in $^{\\mathrm{40}}$Ca$^{\\mathrm{+}}$ is characterized yielding a min...
A Quantum Logic Array Microarchitecture: Scalable Quantum Data Movement and Computation
Metodi, T S; Cross, A W; Chong, F T; Chuang, I L; Metodi, Tzvetan S.; Thaker, Darshan D.; Cross, Andrew W.; Chong, Frederic T.; Chuang, Isaac L.
2005-01-01
Recent experimental advances have demonstrated technologies capable of supporting scalable quantum computation. A critical next step is how to put those technologies together into a scalable, fault-tolerant system that is also feasible. We propose a Quantum Logic Array (QLA) microarchitecture that forms the foundation of such a system. The QLA focuses on the communication resources necessary to efficiently support fault-tolerant computations. We leverage the extensive groundwork in quantum error correction theory and provide analysis that shows that our system is both asymptotically and empirically fault tolerant. Specifically, we use the QLA to implement a hierarchical, array-based design and a logarithmic expense quantum-teleportation communication protocol. Our goal is to overcome the primary scalability challenges of reliability, communication, and quantum resource distribution that plague current proposals for large-scale quantum computing.
Exploring the Quantum Speed Limit with Computer Games
DEFF Research Database (Denmark)
Sørensen, Jens Jakob Winther Hedemann; Pedersen, Mads Kock; Munch, Michael Kulmback
2016-01-01
scientists and allowing them to provide novel solutions to the research problems. Citizen science games have been used successfully in Foldit, EteRNA and EyeWire to study protein and RNA folding and neuron mapping. However, gamification has never been applied in quantum physics. Everyday experiences of non......-experts are based on classical physics and it is \\textit{a priori} not clear that they should have an intuition for quantum dynamics. Does this premise hinder the use of citizen scientists in the realm of quantum mechanics? Here we report on Quantum Moves, an online platform gamifying optimization problems...... in quantum physics. Quantum Moves aims to use human players to find solutions to a class of problems associated with quantum computing. Players discover novel solution strategies which numerical optimizations fail to find. Guided by player strategies, a new low-dimensional heuristic optimization method...
Towards scalable quantum communication and computation: Novel approaches and realizations
Jiang, Liang
Quantum information science involves exploration of fundamental laws of quantum mechanics for information processing tasks. This thesis presents several new approaches towards scalable quantum information processing. First, we consider a hybrid approach to scalable quantum computation, based on an optically connected network of few-qubit quantum registers. Specifically, we develop a novel scheme for scalable quantum computation that is robust against various imperfections. To justify that nitrogen-vacancy (NV) color centers in diamond can be a promising realization of the few-qubit quantum register, we show how to isolate a few proximal nuclear spins from the rest of the environment and use them for the quantum register. We also demonstrate experimentally that the nuclear spin coherence is only weakly perturbed under optical illumination, which allows us to implement quantum logical operations that use the nuclear spins to assist the repetitive-readout of the electronic spin. Using this technique, we demonstrate more than two-fold improvement in signal-to-noise ratio. Apart from direct application to enhance the sensitivity of the NV-based nano-magnetometer, this experiment represents an important step towards the realization of robust quantum information processors using electronic and nuclear spin qubits. We then study realizations of quantum repeaters for long distance quantum communication. Specifically, we develop an efficient scheme for quantum repeaters based on atomic ensembles. We use dynamic programming to optimize various quantum repeater protocols. In addition, we propose a new protocol of quantum repeater with encoding, which efficiently uses local resources (about 100 qubits) to identify and correct errors, to achieve fast one-way quantum communication over long distances. Finally, we explore quantum systems with topological order. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as
Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit
Indian Academy of Sciences (India)
M Ávila
2014-07-01
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 nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic 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. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.
On the Relation Between Quantum Computational Speedup and Retrocausality
Directory of Open Access Journals (Sweden)
Giuseppe Castagnoli
2016-01-01
Full Text Available We investigate the reason for the quantum speedup (quantum algorithms require fewer computation steps than their classical counterparts. We extend the representation of the quantum algorithm to the process of setting the problem, namely choosing the function computed by the black box. The initial measurement selects a setting at random, Bob (the problem setter unitarily changes it into the desired one. With reference to the observer dependent quantum states of relational quantum mechanics, this representation is with respect to Bob and any external observer, it cannot be with respect to Alice (the problem solver. It would tell her the function computed by the black box, which to her should be hidden. To Alice, the projection of the quantum state due to the initial measurement is retarded at the end of her problem solving action, so that the algorithm input state remains one of complete ignorance of the setting. By black box computations, she unitarily sends it into the output state that, for each possible setting, encodes the corresponding solution, acquired by the final measurement. Mathematically, we can ascribe to the final measurement the selection of any fraction R of the random outcome of the initial measurement. This projects the input state to Alice on one of lower entropy where she knows the corresponding fraction of the problem setting. Given the appropriate value of R, the quantum algorithm is a sum over classical histories in each of which Alice, knowing in advance one of the R-th parts of the setting, performs the black box computations still required to identify the solution. Given a quantum algorithm, this retrocausality model provides the value of R that explains its speed up; in the major quantum algorithms, R is 1/2 or slightly above it. Conversely, given the problem, R=1/2 always yields the order of magnitude of the number of black box computations required to solve it in an optimal quantum way.Quanta 2016; 5: 34–52.
Simulation of quantum computation : A deterministic event-based approach
Michielsen, K; De Raedt, K; De Raedt, H
2005-01-01
We demonstrate that locally connected networks of machines that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of quantum computation. We present simulation results for basic quantum operations such as the Hadamard and the controlled-NOT gate, and
A theoretical model of multi-agent quantum computing
Mihelic, F. Matthew
2011-05-01
The best design for practical quantum computing is one that emulates the multi-agent quantum logic function of natural biological systems. Such systems are theorized to be based upon a quantum gate formed by a nucleic acid Szilard engine (NASE) that converts Shannon entropy of encountered molecules into useful work of nucleic acid geometric reconfiguration. This theoretical mechanism is logically and thermodynamically reversible in this special case because it is literally constructed out of the (nucleic acid) information necessary for its function, thereby allowing the nucleic acid Szilard engine to function reversibly because, since the information by which it functions exists on both sides of the theoretical mechanism simultaneously, there would be no build-up of information within the theoretical mechanism, and therefore no irreversible thermodynamic energy cost would be necessary to erase information inside the mechanism. This symmetry breaking Szilard engine function is associated with emission and/or absorption of entangled photons that can provide quantum synchronization of other nucleic acid segments within and between cells. In this manner nucleic acids can be considered as a natural model of topological quantum computing in which the nonabelian interaction of genes can be represented within quantum knot/braid theory as anyon crosses determined by entropic loss or gain that leads to changes in nucleic acid covalent bond angles. This naturally occurring biological form of topological quantum computing can serve as a model for workable man-made multi-agent quantum computing systems.
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; Carlson, Joseph A; Engel, Jonathan; Fann, George; Furnstahl, Richard J; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr; Nazarewicz, Witold; Ng, Esmond G; Nobre, Gustavo P A; Ormand, Erich; Papenbrock, Thomas; Pei, Junchen; Pieper, Steven C; Quaglioni, Sofia; Roche, Kenneth J; Sarich, Jason; Schunck, Nicolas; Sosonkina, Masha; Terasaki, Jun; Thompson, Ian J; Vary, James P; Wild, Stefan M
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Preparing ground States of quantum many-body systems on a quantum computer.
Poulin, David; Wocjan, Pawel
2009-04-03
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time sqrt[N]. Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.
Experimental quantum computing to solve systems of linear equations.
Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei
2013-06-07
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.
Continuous Variable Quantum Communication and Computation
DEFF Research Database (Denmark)
Andersen, Ulrik Lund; Dong, Ruifang; Jezek, Miroslav
2011-01-01
We use squeezed states of light to implement a robust continuous variable quantum key distribution scheme and an optical Hadamard gate based on coherent state qubits.......We use squeezed states of light to implement a robust continuous variable quantum key distribution scheme and an optical Hadamard gate based on coherent state qubits....
Computing protein infrared spectroscopy with quantum chemistry.
Besley, Nicholas A
2007-12-15
Quantum chemistry is a field of science that has undergone unprecedented advances in the last 50 years. From the pioneering work of Boys in the 1950s, quantum chemistry has evolved from being regarded as a specialized and esoteric discipline to a widely used tool that underpins much of the current research in chemistry today. This achievement was recognized with the award of the 1998 Nobel Prize in Chemistry to John Pople and Walter Kohn. As the new millennium unfolds, quantum chemistry stands at the forefront of an exciting new era. Quantitative calculations on systems of the magnitude of proteins are becoming a realistic possibility, an achievement that would have been unimaginable to the early pioneers of quantum chemistry. In this article we will describe ongoing work towards this goal, focusing on the calculation of protein infrared amide bands directly with quantum chemical methods.
Experimental demonstration of a programmable quantum computer by NMR.
Kim, Jaehyun; Lee, Jae-Seung; Hwang, Taesoon; Lee, Soonchil
2004-01-01
A programmable quantum computer is experimentally demonstrated by nuclear magnetic resonance using one qubit for the program and two qubits for data. A non-separable two-qubit operation is performed in a programmable way to show the successful demonstration. Projective measurements required in the programmable quantum computer are simulated by averaging the results of experiments just like when producing an effective pure state.
Time independent universal computing with spin chains: quantum plinko machine
Thompson, K. F.; Gokler, C.; Lloyd, S.; Shor, P. W.
2016-07-01
We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit using g gate blocks on m qubits can be encoded into chains of length O({g}3+δ {m}3+δ ) for all δ \\gt 0 with vanishingly small error.
Thermalization in nature and on a quantum computer.
Riera, Arnau; Gogolin, Christian; Eisert, Jens
2012-02-24
In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
Quantum computation for large-scale image classification
Ruan, Yue; Chen, Hanwu; Tan, Jianing; Li, Xi
2016-10-01
Due to the lack of an effective quantum feature extraction method, there is currently no effective way to perform quantum image classification or recognition. In this paper, for the first time, a global quantum feature extraction method based on Schmidt decomposition is proposed. A revised quantum learning algorithm is also proposed that will classify images by computing the Hamming distance of these features. From the experimental results derived from the benchmark database Caltech 101, and an analysis of the algorithm, an effective approach to large-scale image classification is derived and proposed against the background of big data.
Directory of Open Access Journals (Sweden)
Alexis De Vos
2011-06-01
Full Text Available Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qubit, the transformation being controlled by the other w−1 (qubits. We explain why the former circuit can be decomposed into 2w − 1 control gates, whereas the latter circuit needs 2w − 1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w − 1 or into 2w − 1 control gates.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
Quantum perceptron over a field and neural network architecture selection in a quantum computer.
da Silva, Adenilton José; Ludermir, Teresa Bernarda; de Oliveira, Wilson Rosa
2016-04-01
In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator.
The Rabi Oscillation in Subdynamic System for Quantum Computing
Directory of Open Access Journals (Sweden)
Bi Qiao
2015-01-01
Full Text Available A quantum computation for the Rabi oscillation based on quantum dots in the subdynamic system is presented. The working states of the original Rabi oscillation are transformed to the eigenvectors of subdynamic system. Then the dissipation and decoherence of the system are only shown in the change of the eigenvalues as phase errors since the eigenvectors are fixed. This allows both dissipation and decoherence controlling to be easier by only correcting relevant phase errors. This method can be extended to general quantum computation systems.
Quantum computation with classical light: The Deutsch Algorithm
Energy Technology Data Exchange (ETDEWEB)
Perez-Garcia, Benjamin [Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849 (Mexico); University of the Witwatersrand, Private Bag 3, Johannesburg 2050 (South Africa); Francis, Jason [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); McLaren, Melanie [University of the Witwatersrand, Private Bag 3, Johannesburg 2050 (South Africa); Hernandez-Aranda, Raul I. [Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849 (Mexico); Forbes, Andrew [University of the Witwatersrand, Private Bag 3, Johannesburg 2050 (South Africa); Konrad, Thomas, E-mail: konradt@ukzn.ac.za [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); National Institute of Theoretical Physics, Durban Node, Private Bag X54001, Durban 4000 (South Africa)
2015-08-28
We present an implementation of the Deutsch Algorithm using linear optical elements and laser light. We encoded two quantum bits in form of superpositions of electromagnetic fields in two degrees of freedom of the beam: its polarisation and orbital angular momentum. Our approach, based on a Sagnac interferometer, offers outstanding stability and demonstrates that optical quantum computation is possible using classical states of light. - Highlights: • We implement the Deutsh Algorithm using linear optical elements and classical light. • Our qubits are encoded in the polarisation and orbital angular momentum of the beam. • We show that it is possible to achieve quantum computation with two qubits in the classical domain of light.
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Exponential rise of dynamical complexity in quantum computing through projections.
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-10-10
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.
Scalable Digital Hardware for a Trapped Ion Quantum Computer
Mount, Emily; Vrijsen, Geert; Adams, Michael; Baek, So-Young; Hudek, Kai; Isabella, Louis; Crain, Stephen; van Rynbach, Andre; Maunz, Peter; Kim, Jungsang
2015-01-01
Many of the challenges of scaling quantum computer hardware lie at the interface between the qubits and the classical control signals used to manipulate them. Modular ion trap quantum computer architectures address scalability by constructing individual quantum processors interconnected via a network of quantum communication channels. Successful operation of such quantum hardware requires a fully programmable classical control system capable of frequency stabilizing the continuous wave lasers necessary for trapping and cooling the ion qubits, stabilizing the optical frequency combs used to drive logic gate operations on the ion qubits, providing a large number of analog voltage sources to drive the trap electrodes, and a scheme for maintaining phase coherence among all the controllers that manipulate the qubits. In this work, we describe scalable solutions to these hardware development challenges.
Quantum Computing Resource Estimate of Molecular Energy Simulation
Whitfield, James D; Aspuru-Guzik, Alán
2010-01-01
Over the last century, ingenious physical and mathematical insights paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, efficient methods for the exact simulation of quantum systems on classical computers do not exist. The present paper reports an extension of one of the authors' previous work [Aspuru-Guzik et al., Science {309} p. 1704, (2005)] where it was shown that the chemical Hamiltonian can be efficiently simulated using a quantum computer. In particular, we report in detail how a set of molecular integrals can be used to create a quantum circuit that allows the energy of a molecular system with fixed nuclear geometry to be extracted using the phase estimation algorithm proposed by Abrams and Lloyd [Phys. Rev. Lett. {83} p. 5165, (1999)]. We extend several known results related to this idea and present numerical examples of the state preparation procedure required in the algorithm. With future quantum devices in mind, we provide a compl...
Scalable digital hardware for a trapped ion quantum computer
Mount, Emily; Gaultney, Daniel; Vrijsen, Geert; Adams, Michael; Baek, So-Young; Hudek, Kai; Isabella, Louis; Crain, Stephen; van Rynbach, Andre; Maunz, Peter; Kim, Jungsang
2016-12-01
Many of the challenges of scaling quantum computer hardware lie at the interface between the qubits and the classical control signals used to manipulate them. Modular ion trap quantum computer architectures address scalability by constructing individual quantum processors interconnected via a network of quantum communication channels. Successful operation of such quantum hardware requires a fully programmable classical control system capable of frequency stabilizing the continuous wave lasers necessary for loading, cooling, initialization, and detection of the ion qubits, stabilizing the optical frequency combs used to drive logic gate operations on the ion qubits, providing a large number of analog voltage sources to drive the trap electrodes, and a scheme for maintaining phase coherence among all the controllers that manipulate the qubits. In this work, we describe scalable solutions to these hardware development challenges.
Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious
Cirasella, Jill
2009-01-01
This article presents an annotated selection of the most important and informative Internet resources for learning about quantum computing, finding quantum computing literature, and tracking quantum computing news. All of the quantum computing resources described in this article are freely available, English-language web sites that fall into one…
Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious
Cirasella, Jill
2009-01-01
This article presents an annotated selection of the most important and informative Internet resources for learning about quantum computing, finding quantum computing literature, and tracking quantum computing news. All of the quantum computing resources described in this article are freely available, English-language web sites that fall into one…
Quantum Computation Based on Photons with Three Degrees of Freedom
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun
2016-05-01
Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems.
Fano, Guido
2017-01-01
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...
Globally controlled artificial semiconducting molecules as quantum computers
Tribollet, J
2005-01-01
Quantum computers are expected to be considerably more efficient than classical computers for the execution of some specific tasks. The difficulty in the practical implementation of thoose computers is to build a microscopic quantum system that can be controlled at a larger mesoscopic scale. Here I show that vertical lines of donor atoms embedded in an appropriate Zinc Oxide semiconductor structure can constitute artificial molecules that are as many copy of the same quantum computer. In this scalable architecture, each unit of information is encoded onto the electronic spin of a donor. Contrary to most existing practical proposals, here the logical operations only require a global control of the spins by electromagnetic pulses. Ensemble measurements simplify the readout. With appropriate improvement of its growth and doping methods, Zinc Oxide could be a good semiconductor for the next generation of computers.
Oxford ion-trap quantum computing project.
Lucas, D M; Donald, C J S; Home, J P; McDonnell, M J; Ramos, A; Stacey, D N; Stacey, J-P; Steane, A M; Webster, S C
2003-07-15
We describe recent progress in the development of an ion-trap quantum information processor. We discuss the choice of ion species and describe recent experiments on read-out for a ground-state qubit and photoionization trap loading.
Combined Error Correction Techniques for Quantum Computing Architectures
Byrd, M S; Byrd, Mark S.; Lidar, Daniel A.
2003-01-01
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This us...
Geometric algebra and information geometry for quantum computational software
Cafaro, Carlo
2017-03-01
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of Grover's algorithm, respectively. Specifically, GA is used to describe the Grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target-state before measuring the query register. The transition from digital to analog descriptions occurs via Stone's theorem which relates the (unitary) Grover iterate to a suitable (Hermitian) Hamiltonian that controls Schrodinger's quantum mechanical evolution of a quantum state towards the target state. Once the discrete-to-continuos transition is completed, IG is used to interpret Grover's iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. Finally, we discuss the dissipationless nature of quantum computing, recover the quadratic speedup relation, and identify the superfluity of the Walsh-Hadamard operation from an IG perspective with emphasis on statistical mechanical considerations.
Blind quantum computation over a collective-noise channel
Takeuchi, Yuki; Fujii, Keisuke; Ikuta, Rikizo; Yamamoto, Takashi; Imoto, Nobuyuki
2016-05-01
Blind quantum computation (BQC) allows a client (Alice), who only possesses relatively poor quantum devices, to delegate universal quantum computation to a server (Bob) in such a way that Bob cannot know Alice's inputs, algorithm, and outputs. The quantum channel between Alice and Bob is noisy, and the loss over the long-distance quantum communication should also be taken into account. Here we propose to use decoherence-free subspace (DFS) to overcome the collective noise in the quantum channel for BQC, which we call DFS-BQC. We propose three variations of DFS-BQC protocols. One of them, a coherent-light-assisted DFS-BQC protocol, allows Alice to faithfully send the signal photons with a probability proportional to a transmission rate of the quantum channel. In all cases, we combine the ideas based on DFS and the Broadbent-Fitzsimons-Kashefi protocol, which is one of the BQC protocols, without degrading unconditional security. The proposed DFS-based schemes are generic and hence can be applied to other BQC protocols where Alice sends quantum states to Bob.
Slow phase relaxation as a route to quantum computing beyond the quantum chaos border
Flores, J.; Kun, S. Yu.; Seligman, T. H.
2005-07-01
We reveal that phase memory can be much longer than energy relaxation in systems with exponentially large dimensions of Hilbert space; this finding is documented by 50 years of nuclear experiments, though the information is somewhat hidden. For quantum computers Hilbert spaces of dimension 2100 or larger will be typical and therefore this effect may contribute significantly to reduce the problems of scaling of quantum computers to a useful number of qubits.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Multilinear Formulas and Skepticism of Quantum Computing
Aaronson, S
2003-01-01
Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen Wolfram, have argued that quantum mechanics will break down before the factoring of large numbers becomes possible. If this is true, then there should be a natural "Sure/Shor separator" -- that is, a set of quantum states that can account for all experiments performed to date, but not for Shor's factoring algorithm. We propose as a candidate the set of states expressible by a polynomial number of additions and tensor products. Using a recent lower bound on multilinear formula size due to Raz, we then show that states arising in quantum error-correction require n^{Omega(log n)} additions and tensor products even to approximate, which incidentally yields the first superpolynomial gap between general and multilinear formula size of functions. More broadly, we introduce a complexity classification of pure quantum states, and prove many basic facts about this classification. Our goal is to refine vague ideas about a breakdown of quantum mech...
Dual Field Theories of Quantum Computation
Vanchurin, Vitaly
2016-01-01
Given two quantum states of $N$ q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large $N$ limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an $N+1$ dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an $N$ dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli $Z$ matrices. Since such situation is not generic we call it the $Z$-problem. On the dual field the...
The Magic of Universal Quantum Computing with Permutations
Directory of Open Access Journals (Sweden)
Michel Planat
2017-01-01
Full Text Available The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject. A first classification of a few types of resulting magic states in low dimensions d≤9 is performed.
A New Searching Problem Solved by Quantum Computers
Institute of Scientific and Technical Information of China (English)
闫海洋
2002-01-01
It is well known that a quantum computer can search more quickly than a classical computer while solving the so-called Grover-searching problem. We present a new searching problem which cannot be classified into Grover's problem and can be solved by using the modified searching iterations with the same efficiency as for Grover's problem.
Computational quantum chemistry and adaptive ligand modeling in mechanistic QSAR.
De Benedetti, Pier G; Fanelli, Francesca
2010-10-01
Drugs are adaptive molecules. They realize this peculiarity by generating different ensembles of prototropic forms and conformers that depend on the environment. Among the impressive amount of available computational drug discovery technologies, quantitative structure-activity relationship approaches that rely on computational quantum chemistry descriptors are the most appropriate to model adaptive drugs. Indeed, computational quantum chemistry descriptors are able to account for the variation of the intramolecular interactions of the training compounds, which reflect their adaptive intermolecular interaction propensities. This enables the development of causative, interpretive and reasonably predictive quantitative structure-activity relationship models, and, hence, sound chemical information finalized to drug design and discovery.
D'Ariano, Giacomo Mauro
2010-05-01
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.
Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers
Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen
2017-06-01
The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.
Kochen-Specker Theorem as a Precondition for Quantum Computing
Nagata, Koji; Nakamura, Tadao
2016-12-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Kochen-Specker Theorem as a Precondition for Quantum Computing
Nagata, Koji; Nakamura, Tadao
2016-08-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Continuous-variable quantum computing on encrypted data
Marshall, Kevin; Jacobsen, Christian S.; Schäfermeier, Clemens; Gehring, Tobias; Weedbrook, Christian; Andersen, Ulrik L.
2016-12-01
The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks.
Entanglement-based machine learning on a quantum computer.
Cai, X-D; Wu, D; Su, Z-E; Chen, M-C; Wang, X-L; Li, Li; Liu, N-L; Lu, C-Y; Pan, J-W
2015-03-20
Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing "big data" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning.
Towards a fullerene-based quantum computer
Energy Technology Data Exchange (ETDEWEB)
Benjamin, Simon C [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Ardavan, Arzhang [Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Briggs, G Andrew D [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Britz, David A [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Gunlycke, Daniel [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Jefferson, John [QinetiQ, St Andrews Road, Malvern, WR14 3PS (United Kingdom); Jones, Mark A G [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Leigh, David F [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Lovett, Brendon W [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Khlobystov, Andrei N [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Lyon, S A [Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 (United States); Morton, John J L [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Porfyrakis, Kyriakos [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Sambrook, Mark R [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Tyryshkin, Alexei M [Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 (United States)
2006-05-31
Molecular structures appear to be natural candidates for a quantum technology: individual atoms can support quantum superpositions for long periods, and such atoms can in principle be embedded in a permanent molecular scaffolding to form an array. This would be true nanotechnology, with dimensions of order of a nanometre. However, the challenges of realizing such a vision are immense. One must identify a suitable elementary unit and demonstrate its merits for qubit storage and manipulation, including input/output. These units must then be formed into large arrays corresponding to an functional quantum architecture, including a mechanism for gate operations. Here we report our efforts, both experimental and theoretical, to create such a technology based on endohedral fullerenes or 'buckyballs'. We describe our successes with respect to these criteria, along with the obstacles we are currently facing and the questions that remain to be addressed.
Quantum Computers, Discrete Space, and Entanglement
Pavicic, M
2002-01-01
We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on a quantum system. In doing so we use MMP diagrams and linear algorithms. MMP diagrams are tractable since an n-block of an MMP diagram has n elements while an n-block of a standard lattice diagram has 2^n elements. An immediate test for such an approach is a generation of minimal and arbitrary Kochen-Specker vectors and we present a minimal state-independent Kochen-Specker set of seven vectors from a Hilbert space with more than four dimensions.
Towards a fullerene-based quantum computer
Benjamin, S C; Briggs, G A D; Britz, D A; Gunlycke, D; Jefferson, J; Jones, M A G; Khlobystov, A N; Leigh, D F; Lovett, B W; Lyon, S A; Morton, J J L; Porfyrakis, K; Sambrook, M R; Tyryshkin, A M; Ardavan, Arzhang; Benjamin, Simon C; Britz, David A; Gunlycke, Daniel; Jefferson, John; Jones, Mark A G; Khlobystov, Andrei N; Leigh, David F; Lovett, Brendon W; Morton, John J L; Porfyrakis, Kyriakos; Sambrook, Mark R; Tyryshkin, Alexei M
2005-01-01
Molecular structures appear to be natural candidates for a quantum technology: individual atoms can support quantum superpositions for long periods, and such atoms can in principle be embedded in a permanent molecular scaffolding to form an array. This would be true nanotechnology, with dimensions of order of a nanometre. However, the challenges of realising such a vision are immense. One must identify a suitable elementary unit and demonstrate its merits for qubit storage and manipulation, including input / output. These units must then be formed into large arrays corresponding to an functional quantum architecture, including a mechanism for gate operations. Here we report our efforts, both experimental and theoretical, to create such a technology based on endohedral fullerenes or 'buckyballs'. We describe our successes with respect to these criteria, along with the obstacles we are currently facing and the questions that remain to be addressed.
Quantum information and computation for chemistry
Kais, Sabre; Rice, Stuart A
2014-01-01
Examines the intersection of quantum information and chemical physics The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics. This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science
Scheme for Entering Binary Data Into a Quantum Computer
Williams, Colin
2005-01-01
A quantum algorithm provides for the encoding of an exponentially large number of classical data bits by use of a smaller (polynomially large) number of quantum bits (qubits). The development of this algorithm was prompted by the need, heretofore not satisfied, for a means of entering real-world binary data into a quantum computer. The data format provided by this algorithm is suitable for subsequent ultrafast quantum processing of the entered data. Potential applications lie in disciplines (e.g., genomics) in which one needs to search for matches between parts of very long sequences of data. For example, the algorithm could be used to encode the N-bit-long human genome in only log2N qubits. The resulting log2N-qubit state could then be used for subsequent quantum data processing - for example, to perform rapid comparisons of sequences.
Computational physics simulation of classical and quantum systems
Scherer, Philipp O J
2017-01-01
This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Partial differential equations are treated generally comparing important methods, and equations of motion are solved by a large number of simple as well as more sophisticated methods. Several modern algorithms for quantum wavepacket motion are compared. The first part of the book discusses the basic numerical methods, while the second part simulates classical and quantum systems. Simple but non-trivial examples from a broad range of physical topics offer readers insights into the numerical treatment but also the simulated problems. Rotational motion is studied in detail, as are simple quantum systems. A two-level system in an external field demonstrates elementary principles from quantum optics and simulation of a quantum bit. Principles of molecular dynamics are shown. Modern bounda ry element methods are presented ...
How to simulate a universal quantum computer using negative probabilities
Hofmann, Holger F.
2009-07-01
The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical communication) between the qubits. For a single gate, the probabilities of the three operations are 1, 1 and -1. This decomposition can be applied in a probabilistic simulation of quantum computation by randomly choosing one of the three operations for each gate and assigning a negative statistical weight to the outcomes of sequences with an odd number of negative probability operations. The maximal exponential speed-up of a quantum computer can then be evaluated in terms of the increase in the number of sequences needed to simulate a single operation of the quantum circuit.
Could one make a diamond-based quantum computer?
Stoneham, A Marshall; Harker, A H; Morley, Gavin W
2009-09-09
We assess routes to a diamond-based quantum computer, where we specifically look towards scalable devices, with at least 10 linked quantum gates. Such a computer should satisfy the deVincenzo rules and might be used at convenient temperatures. The specific examples that we examine are based on the optical control of electron spins. For some such devices, nuclear spins give additional advantages. Since there have already been demonstrations of basic initialization and readout, our emphasis is on routes to two-qubit quantum gate operations and the linking of perhaps 10-20 such gates. We analyse the dopant properties necessary, especially centres containing N and P, and give results using simple scoping calculations for the key interactions determining gate performance. Our conclusions are cautiously optimistic: it may be possible to develop a useful quantum information processor that works above cryogenic temperatures.
Linear optical quantum computing in a single spatial mode.
Humphreys, Peter C; Metcalf, Benjamin J; Spring, Justin B; Moore, Merritt; Jin, Xian-Min; Barbieri, Marco; Kolthammer, W Steven; Walmsley, Ian A
2013-10-11
We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.
Introduction to error correcting codes in quantum computers
Salas, P J
2006-01-01
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction will be considered error free. Finally we will relax this non realistic assumption, introducing the quantum fault-tolerant concept. The existence of an error threshold permits to conclude that there is no physical law preventing a quantum computer from being built. An error model based on the depolarizing channel will be able to provide a simple estimation of the storage or memory computation error threshold: < 5.2 10-5. The encoding is made by means of the [[7,1,3
Noise tailoring for scalable quantum computation via randomized compiling
Wallman, Joel J.; Emerson, Joseph
2016-11-01
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors are even partially coherent, they present a major obstacle to performing robust computations. Here, we propose a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged. We prove that this randomization tailors the noise into stochastic Pauli errors, which can dramatically reduce error rates while introducing little or no experimental overhead. Moreover, we prove that our technique is robust to the inevitable variation in errors over the randomizing gates and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity—comparable to fidelities realized in current experiments—are sufficient to achieve fault-tolerant quantum computation. Furthermore, the worst-case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking protocols, enabling a rigorous certification of the performance of a quantum computer.
Three-Dimensional Wiring for Extensible Quantum Computing: The Quantum Socket
Béjanin, J. H.; McConkey, T. G.; Rinehart, J. R.; Earnest, C. T.; McRae, C. R. H.; Shiri, D.; Bateman, J. D.; Rohanizadegan, Y.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.; Mariantoni, M.
2016-10-01
Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error-correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and the measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: the quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum socket is based on spring-mounted microwires—the three-dimensional wires—that push directly on a microfabricated chip, making electrical contact. A small wire cross section (approximately 1 mm), nearly nonmagnetic components, and functionality at low temperatures make the quantum socket ideal for operating solid-state qubits. The wires have a coaxial geometry and operate over a frequency range from dc to 8 GHz, with a contact resistance of approximately 150 m Ω , an impedance mismatch of approximately 10 Ω , and minimal cross talk. As a proof of principle, we fabricate and use a quantum socket to measure high-quality superconducting resonators at a temperature of approximately 10 mK. Quantum error-correction codes such as the surface code will largely benefit from the quantum socket, which will make it possible to address qubits located on a two-dimensional lattice. The present implementation of the socket could be readily extended to accommodate a
Quantum Computing with an Electron Spin Ensemble
DEFF Research Database (Denmark)
Wesenberg, Janus; Ardavan, A.; Briggs, G.A.D.
2009-01-01
We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized...
Realization of Shor's algorithm on an optical quantum computer
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
@@ A research team led by Prof. PAN Jianwei with the University of Science and Technology of China (USTC), CAS has been successful in performing Shor's algorithm, a quantum algorithm for factorization, in an optical quantum computer. The feat is also independently made by another team led by Andrew White from the University of Queensland in Brisbane, Australia. Both results were published in the 19 December, 2007 issue of Physics Review Newsletters.
PEA: Polymorphic Encryption Algorithm based on quantum computation
Komninos, N.; Mantas, G.
2011-01-01
In this paper, a polymorphic encryption algorithm (PEA), based on basic quantum computations, is proposed for the encryption of binary bits. PEA is a symmetric key encryption algorithm that applies different combinations of quantum gates to encrypt binary bits. PEA is also polymorphic since the states of the shared secret key control the different combinations of the ciphertext. It is shown that PEA achieves perfect secrecy and is resilient to eavesdropping and Trojan horse attacks. A securit...
Scalable photonic quantum computation through cavity-assisted interactions.
Duan, L-M; Kimble, H J
2004-03-26
We propose a scheme for scalable photonic quantum computation based on cavity-assisted interaction between single-photon pulses. The prototypical quantum controlled phase-flip gate between the single-photon pulses is achieved by successively reflecting them from an optical cavity with a single-trapped atom. Our proposed protocol is shown to be robust to practical noise and experimental imperfections in current cavity-QED setups.
Entanglement in systems of oscillators and quantum computations
Ozhigov, Yuri I.
2012-01-01
It is shown that quantum devices based only on oscillators cannot serve as the universal quantum computer, despite of entanglement in such devices, which we roughly estimate for the ideal case and for the harmful entanglement with photonic modes. We show that quasi-particles are the native shell for the entanglement already for ground state, in contast to the free electromagnetic field where vacuum state does not produce entanglement at all.
Prime factorization using quantum annealing and computational algebraic geometry
Dridi, Raouf; Alghassi, Hedayat
2017-02-01
We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians.
Prime factorization using quantum annealing and computational algebraic geometry
Dridi, Raouf; Alghassi, Hedayat
2017-01-01
We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians. PMID:28220854
Computer studies of multiple-quantum spin dynamics
Energy Technology Data Exchange (ETDEWEB)
Murdoch, J.B.
1982-11-01
The excitation and detection of multiple-quantum (MQ) transitions in Fourier transform NMR spectroscopy is an interesting problem in the quantum mechanical dynamics of spin systems as well as an important new technique for investigation of molecular structure. In particular, multiple-quantum spectroscopy can be used to simplify overly complex spectra or to separate the various interactions between a nucleus and its environment. The emphasis of this work is on computer simulation of spin-system evolution to better relate theory and experiment.
Topological quantum computing with Read-Rezayi states.
Hormozi, L; Bonesteel, N E; Simon, S H
2009-10-16
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with k>2, k not equal 4. This work extends previous results which only applied to the case k=3 (Fibonacci) and clarifies why, in that case, gate constructions are simpler than for a generic Read-Rezayi state.
Computational electronics semiclassical and quantum device modeling and simulation
Vasileska, Dragica; Klimeck, Gerhard
2010-01-01
Starting with the simplest semiclassical approaches and ending with the description of complex fully quantum-mechanical methods for quantum transport analysis of state-of-the-art devices, Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation provides a comprehensive overview of the essential techniques and methods for effectively analyzing transport in semiconductor devices. With the transistor reaching its limits and new device designs and paradigms of operation being explored, this timely resource delivers the simulation methods needed to properly model state-of
On the Physical Explanation for Quantum Computational Speedup
Cuffaro, Michael E
2013-01-01
The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit a tentative resolution to it. In particular, I argue that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product states. Chapter 2 begins with a discussion of the most popular of the candidate physical explanations for quantum speedup: the many worlds explanation. I argue that unlike the neo-Everettian interpretation of quantum mechanics it does not have the conceptual resources required to overcome the `preferred basis objection'. I further argue that the many worlds explanation, at best, can serve as a good description of the physical process which takes place in so-called network-based computation, but that it is incompatible with other models of comput...
Randomized benchmarking in measurement-based quantum computing
Alexander, Rafael N.; Turner, Peter S.; Bartlett, Stephen D.
2016-09-01
Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.
An Analog Analogue of a Digital Quantum Computation
Farhi, E; Farhi, Edward; Gutmann, Sam
1998-01-01
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >$ is an unknown (normalized) state. We show how to discover $| w >$ by adding a Hamiltonian (independent of $| w >$) and evolving for a time proportional to $N^{1/2}/E$. We show that this time is optimally short. This process is an analog analogue to Grover's algorithm, a computation on a conventional (!) quantum computer which locates a marked item from an unsorted list of N items in a number of steps proportional to $N^{1/2}$.
On the quantum information processing in nuclear magnetic resonance quantum computing experiments
Energy Technology Data Exchange (ETDEWEB)
Azevedo, E.R. de; Bonk, F.A.; Vidoto, E.L.G.; Bonagamba, T.J. [Universidade de Sao Paulo (IFSC/USP), Sao Carlos, SP (Brazil). Inst. de Fisica; Sarthour, R.S.; Guimaraes, A.P.; Oliveira, I.S. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freitas, J.C.C. [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil). Dept. de Fisica
2003-07-01
Full text: Nuclear Magnetic Resonance appeared in the late nineties to be the most promising candidate to run quantum computing algorithms. An impressive number of experiments demonstrating the implementation of all logic gates and quantum algorithms in systems with a small number of qubits stimulated the general excitement about the technique, and greatly promoted the field. Particularly important were those experiments where entanglement of particles were aimed at. Entanglement is the most fundamental (and weird !) aspect of quantum systems, and is at the basis of quantum teleportation and quantum cryptography, yet impossible to prove in NMR experiments. The hardcore of NMR quantum computing are the so-called pseudo-pure states, upon which radiofrequency (RF) pulses act to implement quantum mechanical unitary transformations, promoting changes in both, Zeeman level populations and coherences in the density matrix. Whereas pseudo-pure states are special non-equilibrium diagonal states, coherences encode information about superposition states. Now, one could safely say that the whole business of quantum computing goes about controlling relative ket phases. In spite of the impossibility to univocally associating a given quantum state to a NMR spectrum, it is possible to demonstrate the phase action of RF pulses over relative ket phases, even if no population changes take place. In this talk these issues will be addressed, and we will show experimental results of our own where this is done in the two-qubit quadrupole nuclei {sup 23}Na in C{sub 10}H{sub 21}NaO{sub 4}S liquid crystal. We demonstrate the reversibility of the Hadamard gate, and of a quantum circuit which generates pseudo-Bell states. The success of the operation reaches almost 100% in the case of the state |01+|10, 80% in the cases of |00> + |01> and |10> + |11>, and 65% for the cat-state |00> + |11>. (author)
Resonant Transfer of Excitons and Quantum Computation
Lovett, B; Nazir, A; Kothari, B; Briggs, A; Lovett, Brendon; Reina, John H.; Nazir, Ahsan; Kothari, Beeneet; Briggs, Andrew
2003-01-01
The excitation-energy transfer--the so-called Forster resonant energy transfer--plays a key role in light harvesting processes in photosynthetic organisms in nature. Here we give two methods for performing quantum logic operations by tailoring this interaction. The first implementation uses a coupled quantum dot molecule where the exciton-exciton interaction and the Forster coupling are controlled by means of the dot size, interdot separation, material composition, confinement potential and applied electric field to obtain high fidelity logic. The second proposes the use of biological systems for embodying qubits where, as a result of a stronger Forster interaction, extended exciton states are expected. These states are likely to be more immune to decoherence.
Towards robust dynamical decoupling and high fidelity adiabatic quantum computation
Quiroz, Gregory
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum
Qudit quantum computation in the Jaynes-Cummings model
DEFF Research Database (Denmark)
Mischuck, Brian; Mølmer, Klaus
2013-01-01
We have developed methods for performing qudit quantum computation in the Jaynes-Cummings model with the qudits residing in a finite subspace of individual harmonic oscillator modes, resonantly coupled to a spin-1/2 system. The first method determines analytical control sequences for the one......- and two-qudit gates necessary for universal quantum computation by breaking down the desired unitary transformations into a series of state preparations implemented with the Law-Eberly scheme [ Law and Eberly Phys. Rev. Lett. 76 1055 (1996)]. The second method replaces some of the analytical pulse...
Qudit quantum computation in the Jaynes-Cummings model
DEFF Research Database (Denmark)
Mischuck, Brian; Mølmer, Klaus
2013-01-01
We have developed methods for performing qudit quantum computation in the Jaynes-Cummings model with the qudits residing in a finite subspace of individual harmonic oscillator modes, resonantly coupled to a spin-1/2 system. The first method determines analytical control sequences for the one......- and two-qudit gates necessary for universal quantum computation by breaking down the desired unitary transformations into a series of state preparations implemented with the Law-Eberly scheme [ Law and Eberly Phys. Rev. Lett. 76 1055 (1996)]. The second method replaces some of the analytical pulse...
Adiabatic quantum computing with spin qubits hosted by molecules.
Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji
2015-01-28
A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.
Quantum annealing: The fastest route to quantum computation?
Smorra, C.; Blaum, K.; Bojtar, L.; Borchert, M.; Franke, K. A.; Higuchi, T.; Leefer, N.; Nagahama, H.; Matsuda, Y.; Mooser, A.; Niemann, M.; Ospelkaus, C.; Quint, W.; Schneider, G.; Sellner, S.; Tanaka, T.; Van Gorp, S.; Walz, J.; Yamazaki, Y.; Ulmer, S.
2015-11-01
The Baryon Antibaryon Symmetry Experiment (BASE) aims at performing a stringent test of the combined charge parity and time reversal (CPT) symmetry by comparing the magnetic moments of the proton and the antiproton with high precision. Using single particles in a Penning trap, the proton/antiproton g-factors, i.e. the magnetic moment in units of the nuclear magneton, are determined by measuring the respective ratio of the spin-precession frequency to the cyclotron frequency. The spin precession frequency is measured by non-destructive detection of spin quantum transitions using the continuous Stern-Gerlach effect, and the cyclotron frequency is determined from the particle*s motional eigenfrequencies in the Penning trap using the invariance theorem. By application of the double Penning-trap method we expect that in our measurements a fractional precision of δ g/ g 10-9 can be achieved. The successful application of this method to the antiproton will consist a factor 1000 improvement in the fractional precision of its magnetic moment. The BASE collaboration has constructed and commissioned a new experiment at the Antiproton Decelerator (AD) of CERN. This article describes and summarizes the physical and technical aspects of this new experiment.
Quantum computation with topological codes from qubit to topological fault-tolerance
Fujii, Keisuke
2015-01-01
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
Quantum computing and polynomial equations over the finite field Z_2
Dawson, C M; Hines, A P; Mortimer, D; Nielsen, M A; Osborne, T J; Dawson, Christopher M.; Haselgrove, Henry L.; Hines, Andrew P.; Mortimer, Duncan; Nielsen, Michael A.; Osborne, Tobias J.
2004-01-01
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes.
HiFi-MBQC High Fidelitiy Measurement-Based Quantum Computing using Superconducting Detectors
2016-04-04
computer. We exploit the conceptual framework of measurement - based quantum computation that enables a client to delegate a computation to a quantum...AFRL-AFOSR-UK-TR-2016-0006 HiFi-MBQC High Fidelitiy Measurement - Based Quantum Computing using Superconducting Detectors Philip Walther UNIVERSITT...HiFi-MBQC High Fidelitiy Measurement - Based Quantum Computing using Superconducting Detectors 5a. CONTRACT NUMBER FA8655-11-1-3004 5b. GRANT NUMBER
Distributed quantum computation via optical fibres
Serafini, A; Bose, S; Serafini, Alessio; Mancini, Stefano; Bose, Sougato
2005-01-01
We investigate the possibility of realising effective quantum gates between two atoms in distant cavities coupled by an optical fibre. We show that highly reliable swap and entangling gates are achievable. We exactly study the stability of these gates in presence of imperfections in coupling strengths and interaction times and prove them to be robust. Moreover, we analyse the effect of spontaneous emission and losses and show that such gates are very promising in view of the high level of coherent control currently achievable in optical cavities.
Decoherence and Zeno time in quantum computations
Antoniou, I; Pronko, G; Yarevsky, E
2003-01-01
We analyze the short-time behaviour of the survival probability in the frame of the Friedrichs model for different form factors. We have shown that the probability may not be quadratic for the short times while the quantum Zeno effect (QZE) still exists in this case. We have found that the time when the QZE could be observed is much smaller than usually assumed. We have studied the anti-Zeno era and have estimated its duration. Related decoherence processes are also discussed.
Lattice surgery translation for quantum computation
Herr, Daniel; Nori, Franco; Devitt, Simon J.
2017-01-01
In this paper we outline a method for a compiler to translate any non fault tolerant quantum circuit to the geometric representation of the lattice surgery error-correcting code using inherent merge and split operations. Since the efficiency of state distillation procedures has not yet been investigated in the lattice surgery model, their translation is given as an example using the proposed method. The resource requirements seem comparable or better to the defect-based state distillation process, but modularity and eventual implementability allow the lattice surgery model to be an interesting alternative to braiding.
Quantum computing with an electron spin ensemble.
Wesenberg, J H; Ardavan, A; Briggs, G A D; Morton, J J L; Schoelkopf, R J; Schuster, D I; Mølmer, K
2009-08-14
We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper pair box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.
Quantum Computing via Singlet-Triplet Spin Qubits in Nanowire Double Quantum Dots
Institute of Scientific and Technical Information of China (English)
XUE Peng
2011-01-01
We propose a new structure for quantum computing via spin qubits with high fidelity.Each spin qubit corresponds to two electrons in a nanowire double quantum dot,with the singlet and one of the triplets as the logical qubit states.The entangling gate is effected by virtual charge dipole transitions.We include noise to show the feasibility of this scheme under current experimental conditions.
Quantum computing by optical control of electron spins
Liu, Ren-Bao; Sham, L J
2010-01-01
We review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III-V or II-VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centers in solids such as P-donors in silicon and nitrogen-vacancy centers in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing betwe...
Progress of solid-state quantum computers at NRIM
Kido, G.; Shinagawa, H.; Terai, K.; Hashi, K.; Goto, A.; Yakabe, T.; Takamasu, T.; Uji, S.; Shimizu, T.; Kitazawa, H.
2001-04-01
In the last five years, we have investigated quantum phenomena of low-dimensional materials and strongly correlated electron systems at high-magnetic fields under the Center of Excellence Development Program (COE project) at the National Research Institute for Metal. The second stage towards the realization of the solid-state quantum devices and measurement of the quantum properties began in April of this year. NMR spectra have been studied in CeP and various lithium fluoride crystals in anticipation of the crystal lattice quantum computer. The magneto-transport effect on tiny aluminum devices fabricated on semiconductors has been studied, and negative magnetoresistance has clearly been observed. An SPM which can be operated at various temperatures in the presence of high-magnetic fields has been developed to construct a magnetic resonance force microscope. The magnetic field effect on the magnetic recording pattern of an HDD was clearly measured up to 7 T.
Quantum computer games: Schrödinger cat and hounds
Gordon, Michal; Gordon, Goren
2012-05-01
The quantum computer game 'Schrödinger cat and hounds' is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. 'Schrödinger cat and hounds' demonstrates the effects of superposition, destructive and constructive interference, measurements and entanglement. More advanced concepts, like particle-wave duality and decoherence, can also be taught using the game as a model. The game that has an optimal solution in the classical version, can have many different solutions and a new balance of powers in the quantum world. Game-aided lectures were given to high-school students which showed that it is a valid and entertaining teaching platform.
Entanglement, thermalisation and stationarity The computational foundations of quantum mechanics
Guruprasad, V
2000-01-01
'Tis said, to know others is to be learned, to know oneself, wise - I demonstrate that it could be more fundamental than knowing the rest of nature, by applying classical computational principles and engineering hindsight to derive and explain quantum entanglement, state space formalism and the statistical nature of quantum mechanics. I show that an entangled photon pair is literally no more than a 1-bit hologram, that the quantum state formalism is completely derivable from general considerations of representation of physical information, and that both the probabilistic aspects of quantum theory and the constancy of h are exactly predicted by the thermodynamics of representation, without precluding a fundamental, relative difference in spatial scale between non-colocated observers, leading to logical foundations of relativity and cosmology that show the current thinking in that field to be simplistic and erroneous.
Quantum computing with collective ensembles of multilevel systems.
Brion, E; Mølmer, K; Saffman, M
2007-12-31
We propose a new physical approach for encoding and processing of quantum information in ensembles of multilevel quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism, which restricts the population of each internal state to the values zero and unity. Quantum computers with 10-20 bits can be built via this scheme in single trapped clouds of ground state atoms subject to the Rydberg excitation blockade mechanism, and the linear dependence between register size and the number of internal quantum states in atoms offers realistic means to reach larger registers.
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.
2014-01-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantu...
Continuous-variable quantum computing on encrypted data
DEFF Research Database (Denmark)
Marshall, Kevin; Jacobsen, Christian Scheffmann; Schäfermeier, Clemens
2016-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure...... in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables...... in future cloud-based computing networks....
Is there a speed limit for trapped ion quantum computers?
Lau, Hoi-Kwan
2011-01-01
We investigate a speed limit for quantum processing for trapped ion quantum computers using the Kielpinski-Monroe-Wineland (KMW) architecture. The limiting speed for single-ion shuttling between a storage trap and a logic trap is constrained by the need to avoid excessive ion heating, excessive dephasing and decoherence due to the D.C. Stark effect. We estimate the relative significance of these errors and find that dephasing is dominant. We find that the minimum magnitude of dephasing is quadratic in the time of flight, and an inverse cubic in the operational time scale; from these relations, a limit on the operational speed of ion-trap quantum computers is deduced. Without subsequent phase correction, the maximum speed a qubit can be transferred across a 100 micron-long trap, without excessive error, in about 10 ns for calcium ion and 50 ps for beryllium ion.
Indications for quantum computation requirements from comparative brain analysis
Bernroider, Gustav; Baer, Wolfgang
2010-04-01
Whether or not neuronal signal properties can engage 'non-trivial', i.e. functionally significant, quantum properties, is the subject of an ongoing debate. Here we provide evidence that quantum coherence dynamics can play a functional role in ion conduction mechanism with consequences on the shape and associative character of classical membrane signals. In particular, these new perspectives predict that a specific neuronal topology (e.g. the connectivity pattern of cortical columns in the primate brain) is less important and not really required to explain abilities in perception and sensory-motor integration. Instead, this evidence is suggestive for a decisive role of the number and functional segregation of ion channel proteins that can be engaged in a particular neuronal constellation. We provide evidence from comparative brain studies and estimates of computational capacity behind visual flight functions suggestive for a possible role of quantum computation in biological systems.
From Fermat's last theorem to the quantum computer
Vlasov, A Yu
2003-01-01
Despite of an active work of many researchers in the theory of quantum computations, this area still saves some mysterious charm. It is already an almost common idea, that maybe many fashionable current projects will fade in future, but some absolutely unpredictable applications appear instead. Why such optimistic predictions are legal here, despite of an extreme difficulty to suggest each one new promising quantum algorithm or realistic "industrial" application? One reason -- is very deep contents of this area. It maybe only an extremely unlucky occasion, if such a fundamental thing won't supply us with some bright insights and serious new applications. A sign of such nontrivial contents of a theory -- are unexpected links between different branches of our knowledge. In the present paper is mentioned one such link -- between application of Weyl quantization in the theory of quantum computations and abstract mathematical constructions born in mid of XIX century due to unsuccessful tries to prove Fermat's last...
Towards accurate quantum simulations of large systems with small computers.
Yang, Yonggang
2017-01-24
Numerical simulations are important for many systems. In particular, various standard computer programs have been developed for solving the quantum Schrödinger equations. However, the accuracy of these calculations is limited by computer capabilities. In this work, an iterative method is introduced to enhance the accuracy of these numerical calculations, which is otherwise prohibitive by conventional methods. The method is easily implementable and general for many systems.
Towards accurate quantum simulations of large systems with small computers
Yang, Yonggang
2017-01-01
Numerical simulations are important for many systems. In particular, various standard computer programs have been developed for solving the quantum Schrödinger equations. However, the accuracy of these calculations is limited by computer capabilities. In this work, an iterative method is introduced to enhance the accuracy of these numerical calculations, which is otherwise prohibitive by conventional methods. The method is easily implementable and general for many systems. PMID:28117366
Adapting the traveling salesman problem to an adiabatic quantum computer
Warren, Richard H.
2013-04-01
We show how to guide a quantum computer to select an optimal tour for the traveling salesman. This is significant because it opens a rapid solution method for the wide range of applications of the traveling salesman problem, which include vehicle routing, job sequencing and data clustering.
The Temperature Effects on the Ion Trap Quantum Computer
Institute of Scientific and Technical Information of China (English)
Hongmin; JiatiLIN
2001-01-01
We consider one source of decoherence for a quantum computer composed of many trapped ions due to the thermal effects of the system in the presence of laser-ion interaction.The upper limit of the temperature at which the logical gate operations could be carried out reliably is given,and our result is agreement with the experiment.
A Computational Model for Observation in Quantum Mechanics.
1987-03-16
Computer Science Technical Report No. 191, May 1986. [Feynman63j Feynman , R. P., Leighton, R. B., and Sands, M. The Feynman Lectures on Physics...MIT Artificial Intelligence Laboratory Memo 380, Sept. 1976. [Wheeler83] Wheeler , J. A., and Zurek, W. H. Quantum Theory and Measuremrent 72 .4
Human-competitive evolution of quantum computing artefacts by Genetic Programming.
Massey, Paul; Clark, John A; Stepney, Susan
2006-01-01
We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.
Computational Multiqubit Tunnelling in Programmable Quantum Annealers
2016-08-25
annealing of a 16-qubit problem. Nat. Commun. 4, 1903 (2013). 13. McGeoch, C. C. & Wang, C. in Proceedings of the ACM International Conference on...Computing Frontiers 23 ( ACM , 2013). 14. Dash, S. A note on qubo instances defined on chimera graphs. Preprint at http://arxiv.org/abs/1306.1202 (2013...B. W. in Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing 502–510 (New York, NY, USA, 2004). 33. Somma, R. D., Boixo, S
Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer
Institute of Scientific and Technical Information of China (English)
ZHANG Da-Li; WANG Yan-Hui; ZHANG Yong
2008-01-01
Using cluster state and single qubit measurement one can perform the one-way quantum computation. Here we give a detailed scheme for realizing a modified Grover search algorithm using measurements on cluster state. We give the measurement pattern for the duster-state realization of the algorithm and estimated the number of measurement needed for its implementation. It is found that O(23n/2n2) number of single qubit measurements is required for its realization in a cluster-state quantum computer.
Pauli Exchange Errors in Quantum Computation
Ruskai, M B
2000-01-01
We argue that a physically reasonable model of fault-tolerant computation requires the ability to correct a type of two-qubit error which we call Pauli exchange errors as well as one qubit errors. We give an explicit 9-qubit code which can handle both Pauli exchange errors and all one-bit errors.
Linear Optical Quantum Computing in a Single Spatial Mode
Walmsley, Ian
2014-05-01
We present a scheme for linear optical quantum computing using time-bin encoded qubits in a single spatial mode. This scheme allows arbitrary numbers of qubits to be encoded in the same mode, circumventing the requirement for many spatial modes that challenges the scalability of other schemes, and exploiting the inherent stability and robustness of time-frequency optical modes. This approach leverages the architecture of modern telecommunications systems, and opens a door to very high dimensional Hilbert spaces while maintaining compact device designs. Further, temporal encodings benefit from intrinsic robustness to inhomogeneities in transmission mediums. These advantages have been recognized in works exploring the preparation of time-frequency entangled states both for tests of fundamental quantum phenomena, and for quantum communications technologies including key distribution and teleportation. Here we extend this idea to computation. In particular, we present methods for single-qubit operations and heralded controlled phase (CPhase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn scheme. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84 /pm 0.07. An analysis of the performance of current technologies suggests that our scheme offers a promising route for the construction of quantum circuits beyond the few-qubit level. In addition, we foresee that our investigation may motivate further development of the approaches presented into a regime in which time bins are temporally overlapped and frequency based manipulations become necessary, opening up encodings of even higher densities. This work was supported by the Engineering and Physical Sciences Research Council (EP/H03031X/1), the European Commission project Q-ESSENCE (248095) and the Air Force Office of Scientific Research
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Energy Technology Data Exchange (ETDEWEB)
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
Deterministic Computational Complexity of the Quantum Separability Problem
Ioannou, L M
2006-01-01
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is the quantum separability problem. In Section 1, I begin with a brief introduction to bipartite separability and entanglement, and a basic formal definition of the quantum separability problem. I conclude with a summary of one-sided tests for separability, including those involving semidefinite programming. In Section 2, I treat the separability problem as a computational decision problem and motivate its approximate formulations. After a review of basic complexity-theoretic notions, I discuss the computational complexity of the separability problem (including a Turing-NP-complete formulation of the problem and a proof of "strong NP-hardness" (based on a new NP-hardness proof by Gurvits)). In Section 3, I give a comprehensive survey and complexity analysis of deterministic a...
Computational complexity of nonequilibrium steady states of quantum spin chains
Marzolino, Ugo; Prosen, Tomaž
2016-03-01
We study nonequilibrium steady states (NESS) of spin chains with boundary Markovian dissipation from the computational complexity point of view. We focus on X X chains whose NESS are matrix product operators, i.e., with coefficients of a tensor operator basis described by transition amplitudes in an auxiliary space. Encoding quantum algorithms in the auxiliary space, we show that estimating expectations of operators, being local in the sense that each acts on disjoint sets of few spins covering all the system, provides the answers of problems at least as hard as, and believed by many computer scientists to be much harder than, those solved by quantum computers. We draw conclusions on the hardness of the above estimations.
Novel photonic bandgap based architectures for quantum computers and networks
Guney, Durdu
All of the approaches for quantum information processing have their own advantages, but unfortunately also their own drawbacks. Ideally, one would merge the most attractive features of those different approaches in a single technology. We envision that large-scale photonic crystal (PC) integrated circuits and fibers could be the basis for robust and compact quantum circuits and processors of the next generation quantum computers and networking devices. Cavity QED, solid-state, and (non)linear optical models for computing, and optical fiber approach for communications are the most promising candidates to be improved through this novel technology. In our work, we consider both digital and analog quantum computing. In the digital domain, we first perform gate-level analysis. To achieve this task, we solve the Jaynes-Cummings Hamiltonian with time-dependent coupling parameters under the dipole and rotating-wave approximations for a 3D PC single-mode cavity with a sufficiently high Q-factor. We then exploit the results to show how to create a maximally entangled state of two atoms and how to implement several quantum logic gates: a dual-rail Hadamard gate, a dual-rail NOT gate, and a SWAP gate. In all of these operations, we synchronize atoms, as opposed to previous studies with PCs. The method has the potential for extension to N-atom entanglement, universal quantum logic operations, and the implementation of other useful, cavity QED-based quantum information processing tasks. In the next part of the digital domain, we study circuit-level implementations. We design and simulate an integrated teleportation and readout circuit on a single PC chip. The readout part of our device can not only be used on its own but can also be integrated with other compatible optical circuits to achieve atomic state detection. Further improvement of the device in terms of compactness and robustness is possible by integrating with sources and detectors in the optical regime. In the analog
Quantum computation with Turaev-Viro codes
Koenig, Robert; Reichardt, Ben W
2010-01-01
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For a manifold with boundary, the tensor network has free indices that can be associated to qudits, and its contraction gives the coefficients of a quantum error-correcting code. The code has local stabilizers determined by Levin and Wen. For example, applied to the genus-one handlebody using the Z_2 category, this construction yields the well-known toric code. For other categories, such as the Fibonacci category, the construction realizes a non-abelian anyon model over a discrete lattice. By studying braid group representations acting on equivalence classes of colored ribbon graphs embedded in a punctured sphere, we identify the anyons, and give a simple recipe for mapping fusion basis states of the doubled category to ribbon graphs. We explain how suitable initial states can ...
Efficient quantum algorithm for computing n-time correlation functions.
Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E
2014-07-11
We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.
Discrete Wigner functions and quantum computational speed-up
Galvão, E F
2004-01-01
In quant-ph/0401155 Wootters and colaborators defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speed-up in pure-state quantum computation.
Controllable coherent population transfers in superconducting qubits for quantum computing.
Wei, L F; Johansson, J R; Cen, L X; Ashhab, S; Nori, Franco
2008-03-21
We propose an approach to coherently transfer populations between selected quantum states in one- and two-qubit systems by using controllable Stark-chirped rapid adiabatic passages. These evolution-time insensitive transfers, assisted by easily implementable single-qubit phase-shift operations, could serve as elementary logic gates for quantum computing. Specifically, this proposal could be conveniently demonstrated with existing Josephson phase qubits. Our proposal can find an immediate application in the readout of these qubits. Indeed, the broken parity symmetries of the bound states in these artificial atoms provide an efficient approach to design the required adiabatic pulses.
Loss tolerant one-way quantum computation -- a horticultural approach
Varnava, M; Rudolph, T; Varnava, Michael; Browne, Daniel E.; Rudolph, Terry
2005-01-01
We introduce a scheme for fault tolerantly dealing with losses in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively - no coherent measurements or coherent correction is required. We then use this procedure within a specific linear optical quantum computation proposal to show that: (i) given perfect sources, detector inefficiencies of up to 50% can be tolerated and (ii) given perfect detectors, the purity of the photon source (overlap of the photonic wavefunction with the desired single mode) need only be greater than 66.6% for efficient computation to be possible.
Quantum Computing - A new Implementation of Simon Algorithm for 3-Dimensional Registers
Directory of Open Access Journals (Sweden)
Adina Bărîlă
2015-03-01
Full Text Available Quantum computing is a new field of science aiming to use quantum phenomena in order to perform operations on data. The Simon algorithm is one of the quantum algorithms which solves a certain problem exponentially faster than any classical algorithm solving the same problem. Simulating of quantum algorithms is very important since quantum hardware is not available outside of the research labs. QCL (Quantum Computation Language is the most advanced implemented quantum computer simulator and was conceived by Bernhard Ömer. The paper presents an implementation in QCL of the Simon algorithm in the case of 3-dimensional registers.
Wei, Hai-Rui; Deng, Fu-Guo
2013-07-29
We investigate the possibility of achieving scalable photonic quantum computing by the giant optical circular birefringence induced by a quantum-dot spin in a double-sided optical microcavity as a result of cavity quantum electrodynamics. We construct a deterministic controlled-not gate on two photonic qubits by two single-photon input-output processes and the readout on an electron-medium spin confined in an optical resonant microcavity. This idea could be applied to multi-qubit gates on photonic qubits and we give the quantum circuit for a three-photon Toffoli gate. High fidelities and high efficiencies could be achieved when the side leakage to the cavity loss rate is low. It is worth pointing out that our devices work in both the strong and the weak coupling regimes.
Adaptive quantum computation in changing environments using projective simulation
Tiersch, M.; Ganahl, E. J.; Briegel, H. J.
2015-08-01
Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks.