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1

Digital Repository Infrastructure Vision for European Research (DRIVER)

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.

Li, Shu-shen; Long, Gui-lu; Bai, Feng-shan; Feng, Song-lin; Zheng, Hou-zhi

2001-01-01

2

Digital Repository Infrastructure Vision for European Research (DRIVER)

This research paper gives an overview of quantum computers - description of their operation, differences between quantum and silicon computers, major construction problems of a quantum computer and many other basic aspects. No special scientific knowledge is necessary for the reader.

Avaliani, Archil

2004-01-01

3

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 the...

Steane, Andrew

1997-01-01

4

International Nuclear Information System (INIS)

information theory and quantum mechanics fit together very well. In order to explain their relationship, this 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 Einstein, Podolsky and Rosen (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 next outlined, including qubits and data compression, quantum gates, the 'no cloning' property and teleportation. Quantum cryptography is briefly sketched. The universal quantum computer (QC) is described, based on the Church-Turing principle and a network model of computation. Algorithms for such a computer are discussed, especially those for finding the period of a function, and searching a random list. Such algorithms prove that a QC of sufficiently precise construction is not only fundamentally different from any computer which can only manipulate classical information, but can compute a small class of functions with greater efficiency. This implies that some important computational tasks are impossible for any device apart from a QC. To build a universal QC is well beyond the abilities of current technology. However, the principles of quantum information physics can be tested on smaller devices. The current experimental situation is reviewed, with emphasis on the linear ion trap, high-Q optical cavities, and nuclear magnetic resonance methods. These allow coherent control in a Hilbert space of eight dimensions (three qubits) and should be extendable up to a thousand or more dimensions (10 qubits). Among other things, these systems will allow the feasibility of quantum computing to be assessed. In fact such experiments are so difficult that it seemed likely until recently that a practically useful QC (requiring, say, 1000 qubits) was actually ruled out by considerations of experimental imprecision and the unavoidable coupling between any system and its environment. However, a further fundamental part of quantum information physics provides a solution to this impasse. This is quantum error correction (QEC). An introduction to QEC is provided. The evolution of the QC is restricted to a carefully chosen subspace of its Hilbert space. Errors are almost certain to cause a departure from this subspace. QEC provides a means to detect and undo such departures without upsetting the quantum computation. This achieves the apparently impossible, since the computation preserves quantum coherence even though during its course all the qubits in the computer will have relaxed spontaneously many times. The review concludes with an outline of the main features of quantum information physics and avenues for future research. (author)

5

Digital Repository Infrastructure Vision for European Research (DRIVER)

The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The role of the two basic operations, one-spin rotation and controlled-NOT gates, is analyzed, and some exercises are proposed.

Brassard, Gilles; Chuang, Isaac; Lloyd, Seth; Monroe, Christopher

1998-01-01

6

Quantum Computation and Quantum Information

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in na...

Wang, Yazhen

2012-01-01

7

Digital Repository Infrastructure Vision for European Research (DRIVER)

This article gives an elementary introduction to quantum computing. It is a draft for a book chapter of the "Handbook of Nature-Inspired and Innovative Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M. Eshaghian-Wilner, F. Seredynski (Springer, Berlin Heidelberg New York, 2006).

Eisert, J.; Wolf, M. M.

2004-01-01

8

Physics of quantum computation

International Nuclear Information System (INIS)

In the paper, the modern status of the theory of quantum computation is considered. The fundamental principles of quantum computers and their basic notions such as quantum processors and computational basis states of the quantum Turing machine as well as the quantum Fourier transform are discussed. Some possible experimental realizations on the basis of NMR methods are given

9

Quantum Computing for Computer Architects

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

Metodi, Tzvetan

2011-01-01

10

Digital Repository Infrastructure Vision for European Research (DRIVER)

We describe a quantum computer emulator for a generic, general purpose quantum computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch-Jozsa and Grover's database search algorithm.

Raedt, Hans; Hams, Anthony; Michielsen, Kristel; Raedt, Koen

1999-01-01

11

Quantum robots and quantum computers

Energy Technology Data Exchange (ETDEWEB)

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.

Benioff, P.

1998-07-01

12

Integrable Quantum Computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

Integrable quantum computation is defined as quantum computing via the integrable condition, in which two-qubit gates are either nontrivial unitary solutions of the Yang--Baxter equation or the Swap gate (permutation). To make the definition clear, in this article, we explore the physics underlying the quantum circuit model, and then present a unified description on both quantum computing via the Bethe ansatz and quantum computing via the Yang--Baxter equation.

Zhang, Yong

2011-01-01

13

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusu...

???????, ???? ???????????; ???????, ???? ??????????; Diadechko, Alla Mykolaivna; ????????, ????? ?????????????; ????????, ????? ????????????; Dmitriiev, Artem Volodymyrovych

2010-01-01

14

Quantum information. Teleporation - cryptography - quantum computer

International Nuclear Information System (INIS)

The following topics are dealt with: Reality in the test house, quantum teleportation, 100 years of quantum theory, the reality of quanta, interactionless quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view into the future of quantum optics. (HSI)

15

Quantum computing and spintronics

International Nuclear Information System (INIS)

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

16

Quantum Logic and Quantum Computation

We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers. More specifically, we look for a way to feed a quantum computer with algebraic equations of n-th order underlying an infinite dimensional Hilbert space description of quantum systems. A number of new results on states defined on Hilbert lattices are presented and discussed and a number of recently obtained results in the field of Hilbert space equations are reviewed.

Pavicic, Mladen

2008-01-01

17

Introduction to Quantum Computation

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.

Ekert, A.

18

Algorithms for Quantum Computers

Digital Repository Infrastructure Vision for European Research (DRIVER)

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,...

Smith, Jamie; Mosca, Michele

2010-01-01

19

Quantum information. Teleportation - cryptography - quantum computer

International Nuclear Information System (INIS)

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)

20

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.

Fujii, Toshiyuki; Hatakenaka, Noriyuki

2009-01-01

21

International Nuclear Information System (INIS)

The current proposals for the realization of quantum computer such as NMR, quantum dots and trapped ions are based on the using of an atom or an ion as one qubit. In these proposals a quantum computer consists of several atoms and the coupling between them provides the coupling between qubits necessary for a quantum gate. It is discussed whether a single atom can be used as a quantum computer. One can implement a single qubit in atom as a one-particle electron state and multi-qubit states as multi-particle states. Spin-orbit and spin-spin interactions provide the coupling between qubits. In particular one can use the electron spin resonance to process the information encoded in the hyperfine splitting of atomic energy levels. By using quantum state engineering one can manipulate the internal states of the natural or artificial (quantum dot) atom to make quantum computations

22

Adiabatic topological quantum computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the...

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; Flammia, Steven T.; Neels, Alice

2014-01-01

23

Quantum Computing since Democritus

1. Atoms and the void; 2. Sets; 3. Gödel, Turing, and friends; 4. Minds and machines; 5. Paleocomplexity; 6. P, NP, and friends; 7. Randomness; 8. Crypto; 9. Quantum; 10. Quantum computing; 11. Penrose; 12. Decoherence and hidden variables; 13. Proofs; 14. How big are quantum states?; 15. Skepticism of quantum computing; 16. Learning; 17. Interactive proofs and more; 18. Fun with the Anthropic Principle; 19. Free will; 20. Time travel; 21. Cosmology and complexity; 22. Ask me anything.

Aaronson, Scott

2013-03-01

24

International Nuclear Information System (INIS)

Practical realization of quantum computers will require overcoming decoherence and operational errors, which lead to problems that are more severe than in classical computation. It is shown that arbitrarily accurate quantum computation is possible provided that the error per operation is below a threshold value. 36 refs., 1 fig

25

Secure assisted quantum computation

Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her calculation, or even the function she is trying to compute. We describe an efficient protocol by which Bob can help Alice perform the computation, but there is no way for him to learn anything about it. Furthermore, we show how Alice can efficiently detect whether Bob is honestly helping her or if he is introducing errors.

Childs, A M

2001-01-01

26

Algorithms for Quantum Computers

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).

Smith, Jamie

2010-01-01

27

International Nuclear Information System (INIS)

A quantum computer would put the latest PC to shame. Not only would such a device be faster than a conventional computer, but by exploiting the quantum-mechanical principle of superposition it could change the way we think about information processing. However, two key goals need to be met before a quantum computer becomes reality. The first is to be able to control the state of a single quantum bit (or 'qubit') and the second is to build a two-qubit gate that can produce 'entanglement' between the qubit states. (U.K.)

28

Energy Technology Data Exchange (ETDEWEB)

A quantum computer would put the latest PC to shame. Not only would such a device be faster than a conventional computer, but by exploiting the quantum-mechanical principle of superposition it could change the way we think about information processing. However, two key goals need to be met before a quantum computer becomes reality. The first is to be able to control the state of a single quantum bit (or 'qubit') and the second is to build a two-qubit gate that can produce 'entanglement' between the qubit states. (U.K.)

Milburn, Gerard

2003-10-01

29

Computational quantum field theory

International Nuclear Information System (INIS)

The computational quantum field theory (CQFT) is considered as a part of the computational physics. The main mathematical structures of the CQFT are described in the case of quantum chromodynamics. As examples of the application of the CQFT methods the calculation of the topological susceptibility and the gluon condensates are considered

30

Digital Repository Infrastructure Vision for European Research (DRIVER)

We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design which we employ also demonstrates a signature for quantum parallelism which unambiguously delinea...

Chuang, I. L.; Yamamoto, Y.

1995-01-01

31

Energy Technology Data Exchange (ETDEWEB)

Digital computers are machines that can be programmed to perform logical and arithmetical operations. Contemporary digital computers are universal,'' in the sense that a program that runs on one computer can, if properly compiled, run on any other computer that has access to enough memory space and time. Any one universal computer can simulate the operation of any other; and the set of tasks that any such machine can perform is common to all universal machines. Since Bennett's discovery that computation can be carried out in a non-dissipative fashion, a number of Hamiltonian quantum-mechanical systems have been proposed whose time-evolutions over discrete intervals are equivalent to those of specific universal computers. The first quantum-mechanical treatment of computers was given by Benioff, who exhibited a Hamiltonian system with a basis whose members corresponded to the logical states of a Turing machine. In order to make the Hamiltonian local, in the sense that its structure depended only on the part of the computation being performed at that time, Benioff found it necessary to make the Hamiltonian time-dependent. Feynman discovered a way to make the computational Hamiltonian both local and time-independent by incorporating the direction of computation in the initial condition. In Feynman's quantum computer, the program is a carefully prepared wave packet that propagates through different computational states. Deutsch presented a quantum computer that exploits the possibility of existing in a superposition of computational states to perform tasks that a classical computer cannot, such as generating purely random numbers, and carrying out superpositions of computations as a method of parallel processing. In this paper, we show that such computers, by virtue of their common function, possess a common form for their quantum dynamics.

Lloyd, S.

1992-01-01

32

Energy Technology Data Exchange (ETDEWEB)

Digital computers are machines that can be programmed to perform logical and arithmetical operations. Contemporary digital computers are ``universal,`` in the sense that a program that runs on one computer can, if properly compiled, run on any other computer that has access to enough memory space and time. Any one universal computer can simulate the operation of any other; and the set of tasks that any such machine can perform is common to all universal machines. Since Bennett`s discovery that computation can be carried out in a non-dissipative fashion, a number of Hamiltonian quantum-mechanical systems have been proposed whose time-evolutions over discrete intervals are equivalent to those of specific universal computers. The first quantum-mechanical treatment of computers was given by Benioff, who exhibited a Hamiltonian system with a basis whose members corresponded to the logical states of a Turing machine. In order to make the Hamiltonian local, in the sense that its structure depended only on the part of the computation being performed at that time, Benioff found it necessary to make the Hamiltonian time-dependent. Feynman discovered a way to make the computational Hamiltonian both local and time-independent by incorporating the direction of computation in the initial condition. In Feynman`s quantum computer, the program is a carefully prepared wave packet that propagates through different computational states. Deutsch presented a quantum computer that exploits the possibility of existing in a superposition of computational states to perform tasks that a classical computer cannot, such as generating purely random numbers, and carrying out superpositions of computations as a method of parallel processing. In this paper, we show that such computers, by virtue of their common function, possess a common form for their quantum dynamics.

Lloyd, S.

1992-12-01

33

Duality and Recycling Computing in Quantum Computers

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum computer possesses quantum parallelism and offers great computing power over classical computer \\cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \\cite{r1}. Simply put it, a duality computer is a moving qua...

Long, Gui Lu; Liu, Yang

2007-01-01

34

Parallel Quantum Computing in a Single Ensemble Quantum Computer

Digital Repository Infrastructure Vision for European Research (DRIVER)

We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits can be in pure states while other qubits in mixed states. It enables a single ensemble quantum computer to perform $"$single-instruction-multi-data" type of parallel computation. In Grover's algorithm and Shor's algorithm, parallel quantum computing can provide additional speedup. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As ...

Long, Gui Lu; Xiao, Li

2003-01-01

35

High Performance Quantum Computing

The architecture scalability afforded by recent proposals of a large scale photonic based quantum computer, utilizing the theoretical developments of topological cluster states and the photonic chip, allows us to move on to a discussion of massively scaled Quantum Information Processing (QIP). In this letter we introduce the model for a secure and unsecured topological cluster mainframe. We consider the quantum analogue of High Performance Computing, where a dedicated server farm is utilized by many users to run algorithms and share quantum data. The scaling structure of photonics based topological cluster computing leads to an attractive future for server based QIP, where dedicated mainframes can be constructed and/or expanded to serve an increasingly hungry user base with the ideal resource for individual quantum information processing.

Devitt, Simon J; Nemoto, Kae

2008-01-01

36

Quantum computing with defects

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 defect...

Weber, J. R.; Koehl, W. F.; Varley, J. B.; Janotti, A.; Buckley, B. B.; Walle, C. G.; Awschalom, D. D.

2010-01-01

37

Entanglement and Quantum Computation

We argue that entanglement is the essential non-classical ingredient which provides the computational speed-up in quantum algorithms as compared to algorithms based on the processes of classical physics.

Jozsa, R

1997-01-01

38

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 ...

O Brien, Jeremy L.

2008-01-01

39

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 pr...

Pinski, Sebastian D.

2011-01-01

40

Universal Blind Quantum Computation

Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's inputs, outputs and computation remain private. Recently we proposed a universal unconditionally secure BQC scheme, based on the conceptual framework of the measurement-based quantum computing model, where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Here we present a refinement of the scheme which vastly expands the class of quantum circuits which can be directly implemented as a blind computation, by introducing a new class of resource states which we term dotted-complete graph states and expanding the set of single qubit states the client is required to prepare. These two modifications significantly simplify the overall protocol and remove the previously present restriction that only nearest-neighbor circuits could be implemented as blind computations directly. As an added benefit, the refined protocol admits a substantially more intuitive and simplified verification mechanism, allowing the correctness of a blind computation to be verified with arbitrarily small probability of error.

Fitzsimons, Joseph; Kashefi, Elham

2012-02-01

41

International Nuclear Information System (INIS)

A quantum computer has successfully factorized a number for the first time. Quantum mechanics is an extremely successful theory, but also a troubling one. For many years progress was made by concentrating on the obvious applications, and not worrying too much about the counterintuitive world view that quantum mechanics implies. More recently, however, the development of quantum-information theory has reversed this approach. If we take seriously what quantum mechanics seems to be telling us about the world, we can use this 'quantum weirdness' to do apparently impossible things. Probably the most famous application of quantum mechanics is the quantum computer, which is capable of performing calculations that are impossible with any classical device. At first the questions that quantum computers could tackle were rather esoteric, but in 1994 Peter Shor of AT and T Laboratories showed how a quantum computer could factor large numbers, thus rendering most modern cryptographic systems potentially obsolete. In 1996 David Cory and co-workers at the Massachusetts Institute of Technology (MIT) showed how nuclear magnetic resonance (NMR) - a technique best known for its applications in medical imaging and in chemistry - could be used to build small quantum computers. NMR systems are easily controlled by the magnetic component of electromagnetic fields and are only weakly affected by decoherence, and so progress was extremely rapid. Within two years, several two-qubit computers had been developed, and simple algorithms had been implemented. The race was on to build bigger and better NMR quantum computers, and to use them for more interesting tasks. The lead in this race has been held by several different research groups, but has now been decisively claimed by Isaac Chuang's group at Stanford University and IBM's Almaden Research Center in California. Chuang and co-workers have implemented the simplest example of Shor's quantum-factoring algorithm (L Vandersypen 2001 Nature 414 883). In the April issue of Physics World, Jonathan Jones of Oxford University, UK, describes how Chuang's group factored the number 15 using only seven qubits. (U.K.)

42

An Introduction to Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite...

Yanofsky, Noson S.

2007-01-01

43

Beyond Quantum Computation and Towards Quantum Field Computation

Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and she...

Manoharan, A C

2003-01-01

44

Computational quantum chemistry website

Energy Technology Data Exchange (ETDEWEB)

This report contains the contents of a web page related to research on the development of quantum chemistry methods for computational thermochemistry and the application of quantum chemistry methods to problems in material chemistry and chemical sciences. Research programs highlighted include: Gaussian-2 theory; Density functional theory; Molecular sieve materials; Diamond thin-film growth from buckyball precursors; Electronic structure calculations on lithium polymer electrolytes; Long-distance electronic coupling in donor/acceptor molecules; and Computational studies of NOx reactions in radioactive waste storage.

none,

1997-08-22

45

Computational quantum chemistry website

International Nuclear Information System (INIS)

This report contains the contents of a web page related to research on the development of quantum chemistry methods for computational thermochemistry and the application of quantum chemistry methods to problems in material chemistry and chemical sciences. Research programs highlighted include: Gaussian-2 theory; Density functional theory; Molecular sieve materials; Diamond thin-film growth from buckyball precursors; Electronic structure calculations on lithium polymer electrolytes; Long-distance electronic coupling in donor/acceptor molecules; and Computational studies of NOx reactions in radioactive waste storage

46

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfill their destiny as the world's fastest computing devices. (This paper is an expanded version of remarks that were prepared ...

Preskill, J

1997-01-01

47

Spintronics and Quantum Computing with Quantum Dots

The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our theoretical proposal for using electron spins in quantum dots as quantum bits. We present single- and two qubit gate mechanisms in laterally as well as vertically coupled quantum dots and discuss the possibility to couple spins in quantum dots via superexchange. We further present the recently proposed schemes for using a single quantum dot as spin-filter and spin read-out/memory device.

Recher, P; Levy, J

2000-01-01

48

Quantum Computation and Spin Physics

Digital Repository Infrastructure Vision for European Research (DRIVER)

A brief review is given of the physical implementation of quantum computation within spin systems or other two-state quantum systems. The importance of the controlled-NOT or quantum XOR gate as the fundamental primitive operation of quantum logic is emphasized. Recent developments in the use of quantum entanglement to built error-robust quantum states, and the simplest protocol for quantum error correction, are discussed.

Divincenzo, David P.

1996-01-01

49

Quantum Computations: Fundamentals And Algorithms

Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed. The main blocks of quantum logic, schemes of implementation of quantum calculations, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are concerned. Among them special place is taken by Shor's algorithm of number factorization, Grover's algorithm of unsorted database search and, finally, the most promising in application methods of quantum phenomena simulation, particularly quantum chaos. The most perspective methods of experimental realization of quantum computer, namely nuclear-magnetic resonance and trapped ions realizations, are discussed. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum error correction are described.

Duplij, Steven

2007-01-01

50

Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation

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...

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

51

Quantum computers: Definition and implementations

International Nuclear Information System (INIS)

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

52

Duality and Recycling Computing in Quantum Computers

Quantum computer possesses quantum parallelism and offers great computing power over classical computer \\cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \\cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum compute...

Long, Gui Lu

2007-01-01

53

Holographic quantum computing.

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. PMID:18764313

Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus

2008-07-25

54

Quantum cellular automaton for universal quantum computation

International Nuclear Information System (INIS)

This paper describes a quantum cellular automaton capable of performing universal quantum computation. The automaton has an elementary transition function that acts on Margolus cells of 2x2 qubits, and both the 'quantum input' and the program are encoded in the initial state of the system

55

A Theory of Physical Quantum Computation: The Quantum Computer Condition

In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *Quantum Computer Condition* (QCC), a rigorous mathematical statement that connects the irreversible dynamics of the quantum computing machine, with the reversible operations that comprise the quantum computation intended to be carried out by the quantum computing machine. Armed with the QCC, we derive a powerful result that we call the *Encoding No-Go Theorem*. This theorem gives a precise mathematical statement of the conditions under which fault-tolerant quantum computation becomes impossible in the presence of dissipation and/or decoherence. In connection with this theorem, we explicitly calculate a universal critical damping value for...

Gilbert, G; Thayer, F J; Gilbert, Gerald; Hamrick, Michael

2005-01-01

56

Quantum Annealing and Analog Quantum Computation

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.

Das, Arnab

2008-01-01

57

Scalable Quantum Computing with "Enhancement" Quantum Dots

We propose a novel scheme of solid state realization of a quantum computer based on single spin "enhancement mode" quantum dots as building blocks. In the enhancement quantum dots, just one electron can be brought into initially empty dot, in contrast to depletion mode dots based on expelling of electrons from multi-electron dots by gates. The quantum computer architectures based on depletion dots are confronted by several challenges making scalability difficult. These challenges can be successfully met by the approach based on ehnancement mode, capable of producing square array of dots with versatile functionalities. These functionalities allow transportation of qubits, including teleportation, and error correction based on straightforward one- and two-qubit operations. We describe physical properties and demonstrate experimental characteristics of enhancement quantum dots and single-electron transistors based on InAs/GaSb composite quantum wells. We discuss the materials aspects of quantum dot quantum compu...

Lyanda-Geller, Y B; Yang, M J

2005-01-01

58

In everyday life, practically all the information which is processed, exchanged or stored is coded in the form of discrete entities called bits, which take two values only, by convention 0 and 1. With the present technology for computers and optical fibers, bits are carried by electrical currents and electromagnetic waves corresponding to macroscopic fluxes of electrons and photons, and they are stored in memories of various kinds, for example, magnetic memories. Although quantum physics is the basic physics which underlies the operation of a transistor (Chapter 6) or of a laser (Chapter 4), each exchanged or processed bit corresponds to a large number of elementary quantum systems, and its behavior can be described classically due to the strong interaction with the environment (Chapter 9). For about thirty years, physicists have learned to manipulate with great accuracy individual quantum systems: photons, electrons, neutrons, atoms, and so forth, which opens the way to using two-state quantum systems, such as the polarization states of a photon (Chapter 2) or the two energy levels of an atom or an ion (Chapter 4) in order to process, exchange or store information. In § 2.3.2, we used the two polarization states of a photon, vertical (V) and horizontal (H), to represent the values 0 and 1 of a bit and to exchange information. In what follows, it will be convenient to use Dirac's notation (see Appendix A.2.2 for more details), where a vertical polarization state is denoted by |V> or |0> and a horizontal one by |H> or |1>, while a state with arbitrary polarization will be denoted by |?>. The polarization states of a photon give one possible realization of a quantum bit, or for short a qubit. Thanks to the properties of quantum physics, quantum computers using qubits, if they ever exist, would outperform classical computers for some specific, but very important, problems. In Sections 8.1 and 8.2, we describe some typical quantum algorithms and, in order to do so, we shall not be able to avoid some technical developments. However, these two sections may be skipped in a first reading, as they are not necessary for understanding the more general considerations of Sections 8.3 and 8.4.

Bellac, Michel Le

2014-11-01

59

Quantum Gravity on a Quantum Computer?

EPR-type measurements on spatially separated entangled spin qubits allow one, in principle, to detect curvature. Also the entanglement of the vacuum state is affected by curvature. Here, we ask if the curvature of spacetime can be expressed entirely in terms of the spatial entanglement structure of the vacuum. This would open up the prospect that quantum gravity could be simulated on a quantum computer and that quantum information techniques could be fully employed in the study of quantum gravity.

Kempf, Achim

2013-01-01

60

Quantum Walk Schemes for Universal Quantum Computation

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

Underwood, Michael S.

61

Quantum walks, quantum gates, and quantum computers

International Nuclear Information System (INIS)

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both single-excitation and multiexcitation encodings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included

62

Spin-Based Quantum Dot Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a brief overview of the current theoretical and experimental progresses in the study of quantum dot-based quantum computing schemes, then focus on the spin-based varieties, which are generally regarded as the most scalable because of the relatively long coherence times of electron and nuclear spins. Reviewed topics include spin coherence, spin interaction, spin detection, and the current status of the experimental studies of spin-based quantum computing.

Hu, Xuedong

2004-01-01

63

Quantum computing of semiclassical formulas

Digital Repository Infrastructure Vision for European Research (DRIVER)

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.

Georgeot, Bertrand; Giraud, Olivier

2008-01-01

64

Quantum computing on encrypted data.

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. PMID:24445949

Fisher, K A G; Broadbent, A; Shalm, L K; Yan, Z; Lavoie, J; Prevedel, R; Jennewein, T; Resch, K J

2014-01-01

65

Quantum computation and complexity theory

Digital Repository Infrastructure Vision for European Research (DRIVER)

The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed.

Svozil, K.

1994-01-01

66

Quantum computing with defects.

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. PMID:20404195

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

67

Quantum computing with defects

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-coor...

Weber, J R; Varley, J B; Janotti, A; Buckley, B B; Van de Walle, C G; Awschalom, D D

2010-01-01

68

Pulse controlled noise suppressed quantum computation

To make arbitrarily accurate quantum computation possible, practical realization of quantum computers will require suppressing noise in quantum memory and gate operations to make it below a threshold value. A scheme based on realistic quantum computer models is described for suppressing noise in quantum computation without the cost of stringent quantum computing resources.

Duan, L M; Duan, Lu-Ming; Guo, Guang-Can

1998-01-01

69

Cartoon Computation: Quantum-like computing without quantum mechanics

We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpetation and allows for a cartoon representation.

Aerts, D; Aerts, Diederik; Czachor, Marek

2006-01-01

70

Cartoon Computation: Quantum-like computing without quantum mechanics

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear...

Aerts, Diederik; Czachor, Marek

2006-01-01

71

THE APROACH OF CLASSICAL COMPUTER TO QUANTUM COMPUTER

Directory of Open Access Journals (Sweden)

Full Text Available The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe the diffrences between classical and quantum computers, bit and quantum bit and quantum key distribution.

SEYEDEH MOHADESEH ELTEJA

2013-09-01

72

Quantum Computing's Classical Problem, Classical Computing's Quantum Problem

Digital Repository Infrastructure Vision for European Research (DRIVER)

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly...

Meter, Rodney

2013-01-01

73

Universal quantum computation by discontinuous quantum walk

International Nuclear Information System (INIS)

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum ''walker'' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This ''discontinuous'' quantum walk employs perfect quantum-state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one time step apart.

74

Spintronics and Quantum Dots for Quantum Computing and Quantum Communication

Digital Repository Infrastructure Vision for European Research (DRIVER)

Control over electron-spin states, such as coherent manipulation, filtering and measurement promises access to new technologies in conventional as well as in quantum computation and quantum communication. We review our proposal of using electron spins in quantum confined structures as qubits and discuss the requirements for implementing a quantum computer. We describe several realizations of one- and two-qubit gates and of the read-in and read-out tasks. We discuss recently ...

Burkard, Guido; Engel, Hans-andreas; Loss, Daniel

2000-01-01

75

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.

Vianna, R O; Monken, C H; Vianna, Reinaldo O.; Rabelo, Wilson R. M.

2003-01-01

76

Superconducting Quantum Computing Without Entanglement?

Digital Repository Infrastructure Vision for European Research (DRIVER)

In recent years, quantum computing has promised a revolution in computing performance, based on massive parallelism enabled by many entangled qubits. Josephson junction integrated circuits have emerged as the key technology to implement such a universal digital quantum computer. Indeed, prior experiments have demonstrated simple Josephson qubit configurations with quantized energy levels and long coherence times, which are a necessary prerequisite for a practical quantum com...

Kadin, Alan M.; Kaplan, Steven B.

2014-01-01

77

Are Quantum Computing Models Realistic?

Digital Repository Infrastructure Vision for European Research (DRIVER)

The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics (indistinguishability of particles belonging to the same quantum state), and error correction (current techniques cannot correct all small errors). The initial state in the circuit model computation is obtained by applying potentially imprecise Hadamard gate operations whereas useful quantum computation requires a state with no unc...

Kak, Subhash

2001-01-01

78

Algorithms on ensemble quantum computers.

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 ?(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement. PMID:21475662

Boykin, P Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh

2010-06-01

79

Simulating chemistry using quantum computers

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.

Kassal, Ivan; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán

2010-01-01

80

Local Hamiltonians in Quantum Computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a result about eigenvalue gaps from information theory. I also improve results about simulating quantum circuits with AQC. Second, I look at classically simulating time evolution with l...

Nagaj, Daniel

2008-01-01

81

Time-optimal quantum computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an arbitrary Clifford circuit followed by a layer of independent T gates and any necessary feedforward measurement determined corrective S gates all in the time of a single physical measurement. We assume fast classical processing and classical comm...

Fowler, Austin G.

2012-01-01

82

Computing quantum discord is NP-complete

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-produc...

Huang, Yichen

2013-01-01

83

Programmable architecture for quantum computing

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 the global bus, which generate the cluster states and general multiqubit rotations around the z axis, respectively. QFPGA consists of quantum logic blocks (QLBs) and quantum routing channels (QRCs). The QLB is used to generate a small quantum logic while the QRC is used to combine them properly for larger logic realization. Considering the error accumulating on the qubus, the small logic is the general two-qubit quantum gate. However, for the application such as n-qubit quantum Fourier transform, one QLB can be reconfigured for four-qubit quantum Fourier transform. Although this is an implementation-independent architecture, we still make a rough analysis of its performance based on the qubus system. In a word, QFPGA provides a general architecture to integrate different quantum computing models for efficient quantum logic construction.

Chen, Jialin; Wang, Lingli; Charbon, Edoardo; Wang, Bin

2013-08-01

84

Cartoon computation: quantum-like computing without quantum mechanics

International Nuclear Information System (INIS)

We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed-they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpretation and allows for a cartoon representation. (fast track communication)

85

Quantum computation with graphene nanoribbon

We propose a scalable scheme to implement quantum computation in graphene nanoribbon. It is shown that electron or hole can be naturally localized in each zigzag region for a graphene nanoribbon with a sequence of Z-shaped structure without exploiting any confined gate. An one-dimensional graphene quantum dots chain is formed in such graphene nanoribbon, where electron or hole spin can be encoded as qubits. The coupling interaction between neighboring graphene quantum dots is found to be always-on Heisenberg type. Applying the bang-bang control strategy and decoherence free subspaces encoding method, universal quantum computation is argued to be realizable with the present techniques.

Guo, Guo-Ping; Li, Xiao-Peng; Tu, Tao; Guo, Guang-Can

2008-01-01

86

Digital Repository Infrastructure Vision for European Research (DRIVER)

The problem of quantum test is formally addressed. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. QuFault, the authors software package generates test plans for arbitrary quantum circuits using the very efficient simulator QuIDDPro[1]. The quantum fault table is introduced and mathematically formalized, and the test generation method explained.

Biamonte, Jacob D.; Perkowski, Marek A.

2004-01-01

87

Quantum Information and Computing

Preface -- Coherent quantum control of [symbol]-atoms through the stochastic limit / L. Accardi, S. V. Kozyrev and A. N. Pechen -- Recent advances in quantum white noise calculus / L. Accardi and A. Boukas -- Control of quantum states by decoherence / L. Accardi and K. Imafuku -- Logical operations realized on the Ising chain of N qubits / M. Asano, N. Tateda and C. Ishii -- Joint extension of states of fermion subsystems / H. Araki -- Quantum filtering and optimal feedback control of a Gaussian quantum free particle / S. C. Edwards and V. P. Belavkin -- On existence of quantum zeno dynamics / P. Exner and T. Ichinose -- Invariant subspaces and control of decoherence / P. Facchi, V. L. Lepore and S. Pascazio -- Clauser-Horner inequality for electron counting statistics in multiterminal mesoscopic conductors / L. Faoro, F. Taddei and R. Fazio -- Fidelity of quantum teleportation model using beam splittings / K.-H. Fichtner, T. Miyadera and M. Ohya -- Quantum logical gates realized by beam splittings / W. Freudenberg ... [et al.] -- Information divergence for quantum channels / S. J. Hammersley and V. P. Belavkin -- On the uniqueness theorem in quantum information geometry / H. Hasegawa -- Noncanonical representations of a multi-dimensional Brownian motion / Y. Hibino -- Some of future directions of white noise theory / T. Hida -- Information, innovation and elemental random field / T. Hida -- Generalized quantum turing machine and its application to the SAT chaos algorithm / S. Iriyama, M. Ohya and I. Volovich -- A Stroboscopic approach to quantum tomography / A. Jamiolkowski -- Positive maps and separable states in matrix algebras / A. Kossakowski -- Simulating open quantum systems with trapped ions / S. Maniscalco -- A purification scheme and entanglement distillations / H. Nakazato, M. Unoki and K. Yuasa -- Generalized sectors and adjunctions to control micro-macro transitions / I. Ojima -- Saturation of an entropy bound and quantum Markov states / D. Petz -- An infinite dimensional Laplacian acting on some class of Lévy white noise functionals / K. Saitô -- Structure of linear processes / Si Si and Win Win Htay -- Group theory of dynamical maps / E. C. G. Sudarshan -- On quantum analysis, quantum transfer-matrix method, and effective information entropy / M. Suzuki -- Nonequilibrium steady states for a harmonic oscillator interacting with two bose fields-stochastic limit approach and C* algebraic approach / S. Tasaki and L. Accardi -- Control of decoherence with multipulse application / C. Uchiyama -- Quantum entanglement, purification, and linear-optics quantum gates with photonic qubits / P. Walther and A. Zeilinger -- On quantum mutual type measures and capacity / N. Watanabe.

Accardi, L.; Ohya, Masanori; Watanabe, N.

2006-03-01

88

Fast Quantum Computing with Buckyballs

We have found that encapsulated atoms in fullerene molecules, which carry a spin, can be used for fast quantum computing. We describe the scheme for performing quantum computations, going through the preparation of the qubit state and the realization of a two-qubit quantum gate. When we apply a static magnetic field to each encased spin, we find out the ideal design for the preparation of the quantum state. Therefore, adding to our system a time dependent magnetic field, we can perform a phase-gate. The operational time related to a $\\pi-$phase gate is of the order of $ns$. This finding shows that, during the decoherence time, which is proportional to $\\mu s$, we can perform many thousands of gate operations. In addition, the two-qubit state which arises after a $\\pi-$gate is characterized by a high degree of entanglement. This opens a new avenue for the implementation of fast quantum computation.

Garelli, M S; Garelli, Maria Silvia; Kusmartsev, Feodor V

2005-01-01

89

Gates for Adiabatic Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle of quantum annealing, which implies that a carefully controlled energy solution is optimal and corresponds to minimizing a discrete function. The input function can be influenced by rewards and penalties to favor a solution that meets restrictions that are imposed by the problem. We show how to accomplish this influence for gates in adiabati...

Warren, Richard H.

2014-01-01

90

Robust Quantum Computation with Quantum Dots

Quantum computation in solid state quantum dots faces two significant challenges: Decoherence from interactions with the environment and the difficulty of generating local magnetic fields for the single qubit rotations. This paper presents a design of composite qubits to overcome both challenges. Each qubit is encoded in the degenerate ground-state of four (or six) electrons in a system of five quantum dots arranged in a two-dimensional pattern. This decoherence-free subspace is immune to both collective and local decoherence, and resists other forms of decoherence, which must raise the energy. The gate operations for universal computation are simple and physically intuitive, and are controlled by modifying the tunneling barriers between the dots--Control of local magnetic fields is not required. A controlled-phase gate can be implemented in a single pulse.

Hellberg, C S

2003-01-01

91

Computing quantum eigenvalues made easy

International Nuclear Information System (INIS)

An extremely simple and convenient method is presented for computing eigenvalues in quantum mechanics by representing position and momentum operators in matrix form. The simplicity and success of the method is illustrated by numerical results concerning eigenvalues of bound systems and resonances for Hermitian and non-Hermitian Hamiltonians as well as driven quantum systems. Various MATLAB program codes are listed. (author)

92

Quantum information and computing

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

Ohya, M; Watanabe, N

2006-01-01

93

Quantum chromodynamics with advanced computing

Energy Technology Data Exchange (ETDEWEB)

We survey results in lattice quantum chromodynamics from groups in the USQCD Collaboration. The main focus is on physics, but many aspects of the discussion are aimed at an audience of computational physicists.

Kronfeld, Andreas S.; /Fermilab

2008-07-01

94

Continuous-variable blind quantum computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

Blind quantum computation is a secure delegated quantum computing protocol where Alice who does not have sufficient quantum technology at her disposal delegates her computation to Bob who has a fully-fledged quantum computer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. Protocols of blind quantum computation have been proposed for several qubit measurement-based computation models, such as the graph state model, the Affleck-Kennedy-...

Morimae, Tomoyuki

2012-01-01

95

Quantum Computing with Very Noisy Devices

Digital Repository Infrastructure Vision for European Research (DRIVER)

In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we ...

Knill, E.

2004-01-01

96

Quantum computers in phase space

International Nuclear Information System (INIS)

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to measure directly the Wigner function in a given phase-space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm

97

The unity between quantum field computation, real computation, and quantum computation

It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantum computation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum field computation (as enhanced by Wightman's model of quantum field theory) involves computation over the continuum which is remarkably related to the real computation model of Smale. The latter model was established as a generalization of Turing computation. All this is not surprising since it is well known that the physics of quantum field theory (which includes Einstein's special relativity) contains quantum mechanics which in turn contains classical mechanics. The unity of these computing models, which seem to have grown largely independently, could shed new light into questions of computational complexity, into the central P (Polynomial time) versus NP (Non-deterministic Polynomial time) problem of computer science, and also into the description of Nature by fundamenta...

Manoharan, A C

2001-01-01

98

Quantum Computation with Ballistic Electrons

We describe a solid state implementation of a quantum computer using ballistic single electrons as flying qubits in 1D nanowires. We show how to implement all the steps required for universal quantum computation: preparation of the initial state, measurement of the final state and a universal set of quantum gates. An important advantage of this model is the fact that we do not need ultrafast optoelectronics for gate operations. We use cold programming (or pre-programming), i.e., the gates are set before launching the electrons; all programming can be done using static electric fields only.

Ionicioiu, R; Udrea, F; Ionicioiu, Radu; Amaratunga, Gehan; Udrea, Florin

2001-01-01

99

Adiabatic Cluster State Quantum Computing

Models of quantum computation are important because they change the physical requirements for achieving universal quantum computation (QC). For example, one-way QC requires the preparation of an entangled "cluster" state followed by adaptive measurement on this state, a set of requirements which is different from the standard quantum circuit model. Here we introduce a model based on one-way QC but without measurements (except for the final readout), instead using adiabatic deformation of a Hamiltonian whose initial ground state is the cluster state. This opens the possibility to use the copious results from one-way QC to build more feasible adiabatic schemes.

Bacon, Dave

2009-01-01

100

Quantum Computation and Algorithms

International Nuclear Information System (INIS)

It is now firmly established that quantum algorithms provide a substantial speedup over classical algorithms for a variety of problems, including the factorization of large numbers and the search for a marked element in an unsorted database. In this talk I will review the principles of quantum algorithms, the basic quantum gates and their operation. The combination of superposition and interference, that makes these algorithms efficient, will be discussed. In particular, Grover's search algorithm will be presented as an example. I will show that the time evolution of the amplitudes in Grover's algorithm can be found exactly using recursion equations, for any initial amplitude distribution

101

Information, computing technology, and quantum computing

Energy Technology Data Exchange (ETDEWEB)

Information has long been described by physical structures. The spectacularly successful modern computers use silicon transistors to hold and process information. A number of attempts to repeat the success with other kinds of solid-state devices have failed. The reasons for the unique success of silicon transistors are found in the requirements of computing, the properties of transistors, and the variability in devices manufactured in the large quantities needed to build large computing systems. New challenges will be met in building quantum computers to meet the same requirements. (topical review)

Keyes, Robert W [IBM Research Division, Yorktown, NY 10598 (United States)

2006-05-31

102

Quantum Computation Beyond the Circuit Model

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 general physics audience and discuss existing models of quantum computation. Then, I present three results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Las...

Jordan, Stephen P

2008-01-01

103

Local Hamiltonians in Quantum Computation

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a result about eigenvalue gaps from information theory. I also improve results about simulating quantum circuits with AQC. Second, I look at classically simulating time evolution with local Hamiltonians and finding their ground state properties. I give a numerical method for finding the ground state of translationally invariant Hamiltonians on an infinite tree. This method is based on imaginary time evolution within the Matrix Product State ansatz, and uses a new method for bringing the state back to the ansatz after each imaginary time step. I then use it to investigate the phase transition in the transverse field Ising model on the Bethe lattice. Third, I focus on locally constrained quantum problems Local Hamiltonian ...

Nagaj, Daniel

2008-01-01

104

Geometrical perspective on quantum states and quantum computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge transformations on the connections play a role of unitary quantum operations. Thereby, a geometrical model for quantum computation is presented, which is equivalent to the quantum circuit model. This result shows a geometric way of realizing q...

Chen, Zeqian

2013-01-01

105

Experimental implementations of quantum computers

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum Information, Computation and Complexity * Programme at the Institut Henri Poincaré, January 4th – April 7th, 2006 * Organizers: Ph.Grangier, M.Santha and D.L.Shepelyansky * Lectures have been filmed by Peter Rapcan and Michal Sedlak from Bratislava with the support of the Marie Curie RTN "CONQUEST" A trimester at the Centre Emile Borel - Institut Henri Poincaré is devoted to modern developments in a rapidly growing field of quantum information and com...

Divincenzo, David

2006-01-01

106

Analogical Modeling and Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been successfully applied to a variety of problems in language. Several striking similarities between quantum mechanics and analogical modeling have recently been noted: (1) traditional statistics can be derived from a non-statistical basis by assuming da...

Skousen, Royal

2000-01-01

107

Can quantum chemistry be performed on a small quantum computer?

As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One frequently mentioned application is Feynman's original proposal of simulating quantum systems, and in particular the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantum computer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a ten-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantum computation to become useful for quantum chemistry problems, ...

Wecker, Dave; Clark, Bryan K; Hastings, Matthew B; Troyer, Matthias

2013-01-01

108

Adiabatic quantum computation along quasienergies

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...

Tanaka, Atushi

2009-01-01

109

Decoherence and programmable quantum computation

When coherent states of the electromagnetic field are used to drive the evolution of a quantum computer, a decoherence results due to the back reaction from the qubits onto the fields. We show how to calculate this effect. No assumptions about the environment are necessary, so this represents a useful model to test the fidelity of quantum error correcting codes. We examine two cases of interest. First, the decoherence from the Walsh-Hadamard transformations in Grover's search algorithm is found [Phys. Rev. Lett. 79, 325 (1997)]. Interference effects, and decoherence-dependent phases, are present that could be useful in reducing the decoherence. Second, Shor's fault-tolerant controlled-NOT gate is examined, utilizing frequency-selective pulses [Proceedings, 35th Annual Symposium on Foundations of Computer Science (IEEE Press, New York, 1994), pp. 56-65]. This implementation is found not to be optimal in regards to fault-tolerant quantum computation.

Barnes, Jeff P.; Warren, Warren S.

1999-12-01

110

Reversible computing fundamentals, quantum computing, and applications

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

De Vos, Alexis

2010-01-01

111

Quantum computing of quantum chaos and imperfection effects

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study numerically the imperfection effects in the quantum computing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantum computation errors grow exponentially with the number of qubits in the computer while for the other the growth is polynomial. Certain similarity between classical and quantum computing errors is also discussed.

Song, Pil Hun; Shepelyansky, Dima L.

2000-01-01

112

Interaction-free quantum computation

In this paper, we study the quantum computation realized by an interaction-free measurement (IFM). Using Kwiat et al.'s interferometer, we construct a two-qubit quantum gate that changes one particle's trajectory according to whether or not the other particle exists in the interferometer. We propose a method for distinguishing Bell-basis vectors, each of which consists of a pair of an electron and a positron, by this gate. (This is called the Bell-basis measurement.) This method succeeds with probability 1 in the limit of $N \\to \\infty$, where N is the number of beam splitters in the interferometer. Moreover, we can carry out a controlled-NOT gate operation by the above Bell-basis measurement and the method proposed by Gottesman and Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM. This means that we can execute any quantum algorithm by the IFM.

Azuma, H

2004-01-01

113

Quantum Computing and Number Theory

The prime factorization can be efficiently solved on a quantum computer. This result was given by Shor in 1994. In the first half of this article, a review of Shor's algorithm with mathematical setups is given. In the second half of this article, the prime number theorem which is an essential tool to understand the distribution of prime numbers is given.

Sasaki, Yoshitaka

2013-09-01

114

A Quantum Computer Architecture using Nonlocal Interactions

Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper we propose a physical solution to this problem which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers.

Brennen, G K; Williams, C J; Brennen, Gavin K.; Song, Daegene; Williams, Carl J.

2003-01-01

115

Quantum-computer architecture using nonlocal interactions

International Nuclear Information System (INIS)

Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest-neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper, we propose a physical solution to this problem, which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes, providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers

116

Quantum-computer architecture using nonlocal interactions

Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest-neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper, we propose a physical solution to this problem, which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes, providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers.

Brennen, Gavin K.; Song, Daegene; Williams, Carl J.

2003-05-01

117

Universal quantum computing with nanowire double quantum dots

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show a method for implementing universal quantum computing using of a singlet and triplets of nanowire double quantum dots coupled to a one-dimensional transmission line resonator. This method is attractive for both quantum computing and quantum control with inhibition of spontaneous emission, enhanced spin qubit lifetime, strong coupling and quantum nondemolition measurements of spin qubits. We analyze the performance and stability of all required operations and emphasiz...

Xue, P.

2011-01-01

118

Are quantum walks the saviour of optical quantum computing?

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum walks have emerged as an interesting candidate for the implementation of quantum information processing protocols. Optical implementations of quantum walks have been demonstrated by various groups and some have received high-profile coverage. It is often claimed that quantum walks provide an avenue towards universal quantum computation. In this comment I wish to dispel some misconceptions surrounding the prospects of quantum walks as a route towards universal optical...

Rohde, Peter P.

2010-01-01

119

Fixed-gap adiabatic quantum computation

Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single non-degenerate ground state protected from decohering noise by an energy gap that we argue is system-size-independent. Closely analogous to a traditional electric circuit, it substantially changes the requirements for quantum computer construction, easing measurement, timing, and heating problems. Using the standard adiabatic condition, we present evidence that this design permits "quantum concurrent processing" distributing a quantum computation among extra qubits to perform a quantum algorithm of N gates in an amount of time that scales with the square root of N. One consequence of our work is a fixed gap version of adiabatic quantum computation, which several arguments hinted could be impossible.

Mizel, Ari

2010-01-01

120

Intricacies of quantum computational paths

Graph search represents a cornerstone in computer science and is employed when the best algorithmic solution to a problem consists in performing an analysis of a search space representing computational possibilities. Typically, in such problems it is crucial to determine the sequence of transitions performed that led to certain states. In this work we discuss how to adapt generic quantum search procedures, namely quantum random walks and Grover's algorithm, in order to obtain computational paths. We then compare these approaches in the context of tree graphs. In addition we demonstrate that in a best-case scenario both approaches differ, performance-wise, by a constant factor speedup of two, whilst still providing a quadratic speedup relatively to their classical equivalents. We discuss the different scenarios that are better suited for each approach.

Tarrataca, Luís; Wichert, Andreas

2013-02-01

121

Quantum computation with programmable connections between gates

International Nuclear Information System (INIS)

A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e.g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the quantum switch, which can be programmed to switch the order of two channels with a single use of each one. -- Highlights: ? New model of quantum computation performing tasks not allowed by quantum circuits. ? Task requiring a single oracle evaluation instead of N. ? Computation is based on a new gate called “quantum switch”. ? Quantum switch has been achieved in the quantum optical lab.

122

Cove: A Practical Quantum Computer Programming Framework

While not yet in commercial existence, quantum computers have the ability to solve certain classes of problems that are not efficiently solvable on existing Turing Machine based (classical) computers. For quantum computers to be of use, methods of programming them must exist. Proposals exist for programming quantum computers, but all of the existing ones suffer from flaws that make them impractical in commercial software development environments. Cove is a framework for programming quantum computers that extends existing classical languages to allow for quantum computation, thus providing a quantum computing toolkit for commercial software developers. Since the target users of Cove are commercial developers, it is an object oriented framework that can be used by multiple languages and also places emphasis on complete documentation. The focus of Cove is not so much on the software product, but on the fundamental concepts that make quantum computing practical for common developers.

Purkeypile, Matt

2009-01-01

123

Quantum computation with graphene nanoribbon

We propose a scheme to implement quantum computation in graphene nanoribbon (GNR). It is shown that an electron or hole can be naturally localized in each zigzag region for a GNR with a sequence of Z-shaped structures, without using confined gates. A one-dimensional graphene quantum dot chain is formed in such a GNR, where an electron or hole spin can be used as a qubit. The coupling interaction between neighboring qubits is found to be of the always-on Heisenberg type. By exploiting the bang-bang control strategy and the decoherence-free subspaces encoding method, universal quantum gates are argued to be realizable with the present techniques.

Guo, Guo-Ping; Lin, Zhi-Rong; Tu, Tao; Cao, Gang; Li, Xiao-Peng; Guo, Guang-Can

2009-12-01

124

Quantum computing and information extraction for a dynamical quantum system

Digital Repository Infrastructure Vision for European Research (DRIVER)

We discuss the simulation of a complex dynamical system, the so-called quantum sawtooth map model, on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information for this model. It is possible to simulate the dynamical localization of classical chaos and extract the localization length of the system with quadratic speed up with respect to any known classical computation. We can also compute with algebraic speed up the ...

Benenti, Giuliano; Casati, Giulio; Montangero, Simone

2004-01-01

125

Brain Neurons as Quantum Computers:

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.

Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.

126

Quantum computing and nuclear magnetic resonance

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum information processing is the use of inherently quantum mechanical phenomena to perform information processing tasks that cannot be achieved using conventional classical information technologies. One famous example is quantum computing, which would permit calculations to be performed that are beyond the reach of any conceivable conventional computer. Initially it appeared that actually building a quantum computer would be extremely difficult, but in the last few year...

Jones, Ja

2001-01-01

127

Transparallel mind: Classical computing with quantum power

Digital Repository Infrastructure Vision for European Research (DRIVER)

Inspired by the extraordinary computing power promised by quantum computers, the quantum mind hypothesis postulated that quantum mechanical phenomena are the source of neuronal synchronization which, in turn, might underlie consciousness. Here, I present an alternative inspired by a classical computing method with quantum power. This method relies on distributed representations called hyperstrings. Hyperstrings are superpositions of up to an exponential number of similar str...

Helm, Peter A.

2014-01-01

128

Strengths and Weaknesses of Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time, it is natural to ask whether all of NP can be efficiently solved in quantum polynomial time. In this paper, we address this question by proving that relative ...

Bennett, Charles H.; Bernstein, Ethan; Brassard, Gilles; Vazirani, Umesh

1997-01-01

129

Geometry of discrete quantum computing

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.

Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung

2013-05-01

130

Fault Tolerant Quantum Computation with Constant Error

Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than some constant threshold. The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The result holds also for quantum circuits which operate on nearest neighbors only. To achieve this noise resistance, we use concatenated quantum error correcting codes. The scheme presented is general, and works with all quantum codes that satisfy some restrictions, namely that the code is ``proper''. We present two explicit classes of proper quantum codes. The first example of proper quantum codes generalizes classical secret sharing with polynomials. The second uses a known class of quantum codes and converts it to a proper code. This class is defined over a field with p elements, so the elementary quantum particle is not a qubit but a ``qupit...

Aharonov, D; Aharonov, Dorit; Ben-Or, Michael

1996-01-01

131

Suppression of quantum chaos in a quantum computer hardware

We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos.

Lages, J

2005-01-01

132

Measurement-Only Topological Quantum Computation

We remove the need to physically transport computational anyons from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.

Bonderson, Parsa; Nayak, Chetan

2008-01-01

133

The Quantum Human Computer (QHC) Hypothesis

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…

Salmani-Nodoushan, Mohammad Ali

2008-01-01

134

The Next Generation Computing Brainwave-Quantum Computing

Directory of Open Access Journals (Sweden)

Full Text Available This paper is written to explicate the working of Quantum Computing and its mechanics. Quantum Computing is basically a minute field from Nanotechnology. The main purpose of this paper is to explain an inexperienced user about the technology and principles used while designing the architect of a quantum computer. Operational quantum computers would be a reality in forth coming years by the virtue of new mechanisms to explore and implementations. This paper is sectioned into 7 parts. Part 1 is a brief introduction to Quantum Computing i.e. basic working principle of a Qubit. Part 2 covers Qubit and the architect of the whole system. It also enlightens us about the Qubit in more detail like how data is represented, principles like superposition and state of composite system. Part 3 narrates how quantum Computing can be built using Qubits and applies the above mentioned principles. Part 4 deals with the basic introduction to Quantum Mechanics and some principles like dual nature of light and Uncertainty Principle. Part 5 depicts about the advantages of Quantum Computer over present computing systems. Part 6 discusses the overheads of Quantum Computing. Part 7 describes about implementation of Quantum Computing in today’s world. Finally this paper offers an insight about how and by when we would be able to design a full time Quantum Computer and what are the probable considerations to be taken in to account.

T. Venkat Narayana Rao

2010-12-01

135

Adiabatic quantum computation and quantum annealing theory and practice

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

McGeoch, Catherine C

2014-01-01

136

Quantum machine learning what quantum computing means to data mining

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

Wittek, Peter

2014-01-01

137

Optical quantum computation using cluster States.

We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantum computing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)

Nielsen, Michael A

2004-07-23

138

Parallel computing and quantum chromodynamics

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...

Bowler, K C

1999-01-01

139

Embracing the quantum limit in silicon computing.

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. PMID:22094695

Morton, John J L; McCamey, Dane R; Eriksson, Mark A; Lyon, Stephen A

2011-11-17

140

Robust Ising gates for practical quantum computation

International Nuclear Information System (INIS)

I describe the use of techniques based on composite rotations to combat systematic errors in controlled phase gates, which form the basis of two-qubit quantum logic gates. Although developed and described within the context of nuclear magnetic resonanace quantum computing these sequences should be applicable to any implementation of quantum computation based on Ising couplings. In combination with existing single-qubit gates this provides a universal set of robust quantum logic gates

141

Software Pauli Tracking for Quantum Computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

The realisation of large-scale quantum computing is no longer simply a hardware question. The rapid development of quantum technology has resulted in dozens of control and programming problems that should be directed towards the classical computer science and engineering community. One such problem is known as Pauli tracking. Methods for implementing quantum algorithms that are compatible with crucial error correction technology utilise extensive quantum teleportation protoc...

Paler, Alexandru; Devitt, Simon J.; Nemoto, Kae; Polian, Ilia

2014-01-01

142

Efficient fault-tolerant quantum computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This permits a new analysis of the permissible error rates and minimum overheads for robust quantum computing. It is found that, under the standard noise model of ubiquitous stochasti...

Steane, Andrew M.

1998-01-01

143

Pseudospin and Quantum Computation in Semiconductor Nanostructures

We review the theoretical aspects of pseudospin quantum computation using vertically coupled quantum dots in the quantum Hall regime. We discuss the robustness and addressability of these collective, charge-based qubits. The low energy Hilbert space of a coupled set of qubits yields an effective quantum Ising model tunable through external gates. An experimental prediction of an even-odd effect in the Coulomb blockade spectra of the coupled quantum dot system probes the parameter regime necessary for realization of these qubits.

Scarola, V W; Sarma, S D

2005-01-01

144

Zeno effect for quantum computation and control

It is well known that the quantum Zeno effect can protect specific quantum states from decoherence by using projective measurements. Here we combine the theory of weak measurements with stabilizer quantum error correction and detection codes. We derive rigorous performance bounds which demonstrate that the Zeno effect can be used to protect appropriately encoded arbitrary states to arbitrary accuracy, while at the same time allowing for universal quantum computation or quantum control.

Paz-Silva, G A; Lidar, D A

2011-01-01

145

Contextuality supplies the `magic' for quantum computation

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.

Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph

2014-06-01

146

Mini-maximizing two qubit quantum computations

Two qubit quantum computations are viewed as two player, strictly competitive games and a game-theoretic measure of optimality of these computations is developed. To this end, the geometry of Hilbert space of quantum computations is used to establish the equivalence of game-theoretic solution concepts of Nash equilibrium and mini-max outcomes in games of this type, and quantum mechanisms are designed for realizing these mini-max outcomes.

Khan, Faisal Shah; Phoenix, Simon J. D.

2013-12-01

147

Quantum and classical structures in nondeterminstic computation

In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum theories, classical structures over a space correspond to its orthonormal bases. In the present paper, we show that classical structures in the category of relations correspond to biproducts of abelian groups. Although relations are, of course, not an interesting model of quantum computation, this result has some interesting computational interpretations. If relations are viewed as denotations of nondeterministic programs, it uncovers a wide variety of non-standard quantum structures in this familiar area of classical computation. Ironically, it also opens up a version of what in philosophy of quantum mechanics would be called an ontic-epistemic gap, as it provides no interface to these nonstandard quantum structures.

Pavlovic, Dusko

2008-01-01

148

Quantum Computing in Solid State Systems

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.

Ruggiero, B; Granata, C

2006-01-01

149

Quantum Computational Logics and Possible Applications

In quantum computational logics meanings of formulas are identified with quantum information quantities: systems of qubits or, more generally, mixtures of systems of qubits. We consider two kinds of quantum computational semantics: (1) a compositional semantics, where the meaning of a compound formula is determined by the meanings of its parts; (2) a holistic semantics, which makes essential use of the characteristic “holistic” features of the quantum-theoretic formalism. The compositional and the holistic semantics turn out to characterize the same logic. In this framework, one can introduce the notion of quantum-classical truth table, which corresponds to the most natural way for a quantum computer to calculate classical tautologies. Quantum computational logics can be applied to investigate different kinds of semantic phenomena where holistic, contextual and gestaltic patterns play an essential role (from natural languages to musical compositions).

Chiara, Maria Luisa Dalla; Giuntini, Roberto; Leporini, Roberto; di Francia, Giuliano Toraldo

2008-01-01

150

Computing quantum discord is NP-complete

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some entanglement measures (namely entanglement cost, entanglement of formation, relative entropy of entanglement, squashed entanglement, classical squashed entanglement, conditional entanglement of mutual information, and broadcast regularization of mutual information) and constrained Holevo capacity are NP-hard/NP-complete to compute. These complexity-theoretic results are directly applicable in common randomness distillation, quantum state merging, entanglement distillation, superdense coding, and quantum teleportation; they may offer significant insights into quantum information processing. Moreover, we prove the NP-completeness of two typical problems: linear optimization over classical states and detecting classical states in a convex set, providing evidence that working with classical states is generically computationally intractable.

Huang, Yichen

2014-03-01

151

Experimental realization of nonadiabatic holonomic quantum computation.

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. PMID:23705695

Feng, Guanru; Xu, Guofu; Long, Guilu

2013-05-10

152

The Heisenberg representation of quantum computers

Energy Technology Data Exchange (ETDEWEB)

Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.

Gottesman, D.

1998-06-24

153

How to test the “quantumness” of a quantum computer?

Directory of Open Access Journals (Sweden)

Full Text Available Recent devices, using hundreds of superconducting quantum bits, claim to perform quantum computing. However, it is not an easy task to determine and quantify the degree of quantum coherence and control used by these devices. Namely, it is a difficult task to know with certainty whether or not a given device (e.g., the D-Wave One or D-Wave Two is a quantum computer. Such a verification of quantum computing would be more accessible if we already had some kind of working quantum computer, to be able to compare the outputs of these various computing devices. Moreover, the verification process itself could strongly depend on whether the tested device is a standard (gate-based or, e.g., an adiabatic quantum computer. Here we do not propose a technical solution to this quantum-computing “verification problem”, but rather outline the problem in a way which would help both specialists and non-experts to see the scale of this difficult task, and indicate some possible paths towards its solution.

AlexandreM.Zagoskin

2014-05-01

154

Pseudospin Quantum Computation in Semiconductor Nanostructures

We theoretically show that spontaneously interlayer-coherent vertically coupled bilayer quantum Hall droplets should allow robust and fault-tolerant pseudospin quantum computation in semiconductor nanostructures with voltage-tuned external gates providing qubit control and a quantum Ising Hamiltonian providing qubit entanglement. Using a spin-boson model we estimate decoherence to be small (~10^{-5}).

Scarola, V W; Sarma, S D

2003-01-01

155

Natural and artificial atoms for quantum computation

Remarkable progress towards realizing quantum computation has been achieved using natural and artificial atoms. 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.

Buluta, Iulia; Nori, Franco

2010-01-01

156

At the intersection of quantum computing and quantum chemistry

Quantum chemistry is concerned with solving the Schrodinger equation for chemically relevant systems. This is typically done by making useful and systematic approximations which form the basis for model chemistries. A primary contribution of this dissertation, is taking concrete steps toward establishing a new model chemistry based on quantum computation. Electronic energies of the system can be efficiently obtained to fixed accuracy using quantum algorithms exploiting the ability of quantum computers to efficiently simulate the time evolution of quantum systems. The quantum circuits for simulation of arbitrary electronic Hamiltonians are given using quantum bits associated with single particle basis functions. This model chemistry is applied to hydrogen molecule as a case study where all necessary quantum circuits are clearly laid out. Furthermore, our collaboration to experimentally realize a simplified version of the hydrogen molecule quantum circuit is also included in this thesis. Finally, alternatives to the gate model of quantum computation are pursued by exploring models based on the quantum adiabatic theorem and on the generalization of random walks.

Whitfield, James Daniel

157

Parallel Quantum Computation and Quantum Codes

We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding and decoding standard quantum error-correcting codes, or more generally any circuit consisting of controlled-not gates, controlled pi-shifts, and Hadamard gates. Finally, while we note the Quantum Fourier Transform can be parallelized to linear depth, we conjecture that an even simpler `staircase' circuit cannot be parallelized to less than linear depth, and might be used to prove that QNC < QP.

Moore, Cristopher; Moore, Cristopher; Nilsson, Martin

1998-01-01

158

Models of continuous-variable quantum computing

International Nuclear Information System (INIS)

We discuss strictly efficient models for measurement-based quantum computing using physical continuous variables, such as field modes of light. Such measurement-based quantum computing (MBQC) provides a promising paradigm for quantum computation as it does not require performing unitary gates during the computation, but rather appropriate readout. Here, we introduce novel schemes for which the resource state can be reasonably and efficiently prepared, and which notably do not require having infinite squeezing or mean energy available. What is more, error correction techniques are implementable, as the logical information is stored in finite-dimensional objects grasping correlations of the quantum states. Using the ideas of computational tensor networks we discuss how to sequentially prepare suitable physical resource states with cavity QED or with non-linear optics and how to efficiently implement a computational universal set of quantum operations with feasible optical measurements like homodyne detection and photon counting

159

Quantum computation from a quantum logical perspective

Digital Repository Infrastructure Vision for European Research (DRIVER)

It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the information-processing in the three algorithms are presented from a different perspective, in terms of the way in which the algorithms exploit the non-Boolean quantum logic represented by the projective geometry of Hilbert space. From this quantum logical ...

Bub, Jeffrey

2006-01-01

160

Quantum computer of wire circuit architecture

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...

Moiseev, S A; Andrianov, S N

2010-01-01

161

The potential of the quantum computer

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...

2006-01-01

162

Evolutionary Design in Biological Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

The unique capability of quantum mechanics to evolve alternative possibilities in parallel is appealing and over the years a number of quantum algorithms have been developed offering great computational benefits. Systems coupled to the environment lose quantum coherence quickly and realization of schemes based on unitarity might be impossible. Recent discovery of room temperature quantum coherence in light harvesting complexes opens up new possibilities to borrow concepts fr...

Vattay, Gabor; Kauffman, Stuart A.

2013-01-01

163

Fault tolerant dynamical decoupling for quantum computing and quantum memory

Dynamical decoupling (DD) is a popular technique for protecting quantum information from degradation by interactions with the environment. However, unless special care is taken, unavoidable 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 dynamical decoupling sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment, which poses the most challenging regime for protecting quantum information. We present experimental data from nuclear spin qubits in a solid and introduce a new DD sequence that is suitable for quantum computing and quantum memory.

Souza, Alexandre M; Suter, Dieter

2011-01-01

164

Fault-tolerant holonomic quantum computation

We explain how to combine holonomic quantum computation (HQC) with fault tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of computation, while retaining the inherent robustness the method derives from its geometric nature.

Oreshkov, Ognyan; Lidar, Daniel A

2008-01-01

165

Non-adiabatic holonomic quantum computation

International Nuclear Information System (INIS)

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level ? configuration. Our scheme opens up the possibility of realizing universal holonomic quantum computation on qubits characterized by short coherence time. (paper)

166

Error correction in adiabatic quantum computation

In conventional quantum computing models (e.g. the circuit-model) it is well understood that error suppression techniques by themselves are insufficient for fault-tolerant quantum computing. From a thermodynamic perspective this is because error suppression alone does not provide a mechanism to remove the entropy generated by errors from the encoded system . Since the thermodynamic argument is independent of the computational model it is expected that error suppression alone is insufficient for fault-tolerant quantum computing in the adiabatic quantum computing (AQC) model also. In this talk we provide a scheme for performing error correction for AQC and discuss the differences between our method and those used in quantum circuit model implementations.

Young, Kevin; Sarovar, Mohan; Blume-Kohout, Robin

2013-03-01

167

Experimental demonstration of deterministic one-way quantum computation on a NMR quantum computer

International Nuclear Information System (INIS)

One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report an experimental realization of the complete process of deterministic one-way quantum Deutsch-Josza algorithm in NMR, including graph state preparation, single-qubit measurements, and feed-forward corrections. The findings in our experiment may shed light on the future scalable one-way quantum computation.

168

It is shown in the paper that in quantum mechanics the unitary quantum dynamics is the universal quantum driving force to speed up a quantum computation. This assertion supports strongly in theory that the unitary quantum dynamics is the fundamental and universal principle in nature. A new quantum-computing speedup theory is set up on the basis of the unitary quantum dynamics. Both the unitary quantum dynamics and the symmetric structure and property of Hilbert space of a composite quantum system are mainly responsible for an exponential quantum-computing speedup for a general efficient quantum algorithm, while the latter one is the quantum-computing resource which is not owned by the classical computation. The inherent importance for the unitary quantum dynamics to speed up a quantum computation lies in the unique ability of the unitary quantum dynamics to build up the effective interaction between the symmetric structure and property of the Hilbert space of a quantum system and the mathematical symmetric st...

Miao, Xijia

2011-01-01

169

Simulated Quantum Computation of Molecular Energies

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.

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

170

Lyapunov Control of Quantum Systems with Applications to Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

In the design of complex quantum systems like ion traps for quantum computing, it is usually desired to stabilize a particular system state or make the system state track a desired trajectory. Several control theoretical approaches based on feedback seem attractive to solve such problems. But the uncertain dynamics introduced by measurement on quantum systems makes the synthesis of feedback control laws very complicated. Although we have not explicitly modeled the change in ...

Nagarjun, K. P.; Sivaranjani, S.; Koshy, George

2012-01-01

171

Verification of Linear Optical Quantum Computing using Quantum Process Calculus

Digital Repository Infrastructure Vision for European Research (DRIVER)

We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and prove that they are behaviourally equivalent. We extend the theory of behavioural equivalence in the process calculus Communicating Quantum Processes (CQP) to include multiple particles (namely photons) as information carriers, described by ...

Franke-arnold, Sonja; Gay, Simon J.; Puthoor, Ittoop Vergheese

2014-01-01

172

Graph isomorphism and adiabatic quantum computing

In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G ?G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap ? (N) separating the ground and first-excited states in the limit of large problem size N ?1. Calculating ? (N) in this limit is a fundamental open problem in adiabatic quantum computing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantum computing has been shown to be equivalent to the circuit model of quantum computing, and so development of adiabatic quantum algorithms continues to be of great interest.

Gaitan, Frank; Clark, Lane

2014-02-01

173

Effective Pure States for Bulk Quantum Computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 Cory et al. (spatial averaging) for the case ...

Knill, Emanuel; Chuang, Isaac; Laflamme, Raymond

1997-01-01

174

Quantum Computation Using Optically Coupled Quantum Dot Arrays

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.

Pradhan, Prabhakar; Anantram, M. P.; Wang, K. L.; Roychowhury, V. P.; Saini, Subhash (Technical Monitor)

1998-01-01

175

Fault tolerant quantum computation with nondeterministic gates.

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. PMID:21231569

Li, Ying; Barrett, Sean D; Stace, Thomas M; Benjamin, Simon C

2010-12-17

176

Principles of quantum computation and information

Quantum computation and information is a new, rapidly developing interdisciplinary field. Therefore, it is not easy to understand its fundamental concepts and central results without facing numerous technical details. This book provides the reader a useful and not-too-heavy guide. It offers a simple and self-contained introduction; no previous knowledge of quantum mechanics or classical computation is required. Volume I may be used as a textbook for a one-semester introductory course in quantum information and computation, both for upper-level undergraduate students and for graduate students.

Benenti, Giuliano; Strini, Giuliano

2004-01-01

177

One-way quantum computation with circuit quantum electrodynamics

International Nuclear Information System (INIS)

In this Brief Report, we propose a potential scheme to implement one-way quantum computation with circuit quantum electrodynamics (QED). Large cluster states of charge qubits can be generated in just one step with a superconducting transmission line resonator (TLR) playing the role of a dispersive coupler. A single-qubit measurement in the arbitrary basis can be implemented using a single electron transistor with the help of one-qubit gates. By examining the main decoherence sources, we show that circuit QED is a promising architecture for one-way quantum computation.

178

Relating computational complexity and quantum spectral complexity

We present a conjecture and hypothesis regarding complex spectral measures of computations of varying degrees of difficulty. Earlier work based on the study of quantal chaotic and weakly disordered systems has established that irregular spectral fluctuations have a distribution predicted by random matrix theory, while regular spectral fluctuations are given by the Poisson distribution. We elucidate the correlation between random matrix theory and computational complexity and formalize the idea to a conjecture and experimental prediction regarding spectral regularity and computational complexity (NP-complete class) viz. the quantum adiabatic computation algorithm. We show how the result takes the form of a correspondence principle for computational systems between the quantum and classical domains.

Mitchell, David R

2008-01-01

179

Quantum Field Symbolic Analog Computation Relativity Model

It is natural to consider a quantum system in the continuum limit ofspace-time configuration. Incorporating also, Einstein's special relativity,leads to the quantum theory of fields. Non-relativistic quantum mechanics andclassical mechanics are special cases. By studying vacuum expectation values(Wightman functions W(n; z) where z denotes the set of n complex variables) ofproducts of quantum field operators in a separable Hilbert space, one is led tocomputation of holomorphy domains for these functions over the space of severalcomplex variables, C^n. Quantum fields were reconstructed from these functionsby Wightman. Computer automation has been accomplished as deterministic exactanalog computation (computation over "cells" in the continuum of C^n) forobtaining primitive extended tube domains of holomorphy. This is done in a onedimensional space plus one dimensional time model. By considering boundaryrelated semi-algebraic sets, some analytic extensions of these domains areobtained by non-deterministic methods...

Manoharan, A C

2000-01-01

180

Preparing topological PEPS on a quantum computer

Digital Repository Infrastructure Vision for European Research (DRIVER)

Simulating of exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states -- the G-injective Projected Entangled Pair States (PEPS) -- on a quantum computer. Important examples include the resonant valence bond (RVB) states, conjectured to be topological spin liquids. The runtime of the al...

Schwarz, Martin; Cubitt, Toby S.; Temme, Kristan; Verstraete, Frank; Perez-garcia, David

2012-01-01

181

Efficient quantum computing with weak measurements

Digital Repository Infrastructure Vision for European Research (DRIVER)

Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not deeply explored. We examine this issue by giving an example of how to perform the quantum ordering finding algorithm efficiently using non-local weak measurements given that the measurements used are of bounded weakness and some fixed but arbit...

Lund, A. P.

2011-01-01

182

Universal Holonomic Quantum Computation on Spin Chains

We find exact solutions for a universal set of holonomic quantum gates on a scalable candidate for quantum computers, namely an array of two level systems. Previously these gates have been constructed mostly on non-scalable systems and by numerical searches in the space of loops in the space of control parameters of the Hamiltonian.

Karimipour, V

2005-01-01

183

Is the Brain a Quantum Computer?

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…

Litt, Abninder; Eliasmith, Chris; Kroon, Frederick W.; Weinstein, Steven; Thagard, Paul

2006-01-01

184

Distributed quantum computing with single photon sources

International Nuclear Information System (INIS)

Full text: Distributed quantum computing requires the ability to perform nonlocal gate operations between the distant nodes (stationary qubits) of a large network. To achieve this, it has been proposed to interconvert stationary qubits with flying qubits. In contrast to this, we show that distributed quantum computing only requires the ability to encode stationary qubits into flying qubits but not the conversion of flying qubits into stationary qubits. We describe a scheme for the realization of an eventually deterministic controlled phase gate by performing measurements on pairs of flying qubits. Our scheme could be implemented with a linear optics quantum computing setup including sources for the generation of single photons on demand, linear optics elements and photon detectors. In the presence of photon loss and finite detector efficiencies, the scheme could be used to build large cluster states for one way quantum computing with a high fidelity. (author)

185

Basics for Algorithms in Quantum Computing

A short introduction to Quantum Computing, regarded as a paradigm of "parallel computing based on exterior algebras", is presented from the point of view of its main algorithms including the primitive functions, the compositional schemes and the input and output data coding. In this study the Exterior Algebra notation is used in lieu of the more conventional Dirac's ket notation. The basic notions of Exterior Algebra and Hilbert Spaces are sketched in order to show the qubits as points in the unit circle in the two-dimensional complex Hilbert space H1, and any word consisting of qubits as a point in the unit sphere of a external product of H1. The computing procedure is illustrated through the classical Deutsch-Josza's algorithm, followed by the quantum algorithm to compute the Discrete Fourier Transform in linear time and the famous polynomial-time Shor's Algorithm for integer factorization. Finally, basic notions in Quantum Cryptography and Quantum Communication Complexity are discussed.

Morales-Luna, Guillermo

2006-01-01

186

Thermal Noise on Adiabatic Quantum Computation

The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the minimal energy gap. However, at finite temperatures, it might need to be fast enough to avoid thermal excitations. The question is, how fast does it need to be? The structure of evolution Hamiltonians for AQC is generally too complicated for answering this question. Here we model an adiabatic quantum computer as a (parametrically driven) harmonic oscillator. The advantages of this model are (1) it offers high flexibility for quantitative analysis on the thermal effect, (2) the results qualitatively agree with previous numerical calculation, and (3) it could be experimentally verified with quantum electronic circuits.

Yung, Man-Hong

2008-01-01

187

Quantum Computing and Shor`s Factoring Algorithm

Digital Repository Infrastructure Vision for European Research (DRIVER)

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.

Volovich, Igor V.

2001-01-01

188

Elements of quantum computing history, theories and engineering applications

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.

Akama, Seiki

2015-01-01

189

Methodological testing: Are fast quantum computers illusions?

International Nuclear Information System (INIS)

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.

190

Quantum computation and optimized error correction

Two subjects in the area of quantum computation are considered here. In the first chapter I present a universal model for a quantum Robot. Chapters two, three, and four are dedicated to the problem of quantum error correction/protection. A quantum robot is described as a quantum system that moves in, and interacts with, an external environment of quantum systems. Such environments consist of arbitrary numbers and types of particles in two or three dimensional space lattices. I find a set of universal operations that enables the quantum robot to simulate arbitrary quantum dynamics. A computational approach to the quantum error correction problem is presented in chapters two and three. I develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. This theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. I demonstrate via numerical examples that such optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. In the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. I show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block. However, this conclusion breaks down in the presence of an initial entanglement between the encoding and recovery ancillas. Such entanglement assisted error correction procedures are studied in chapter three. I show how entanglement can increase fidelity in the optimized setting by improving the function of the recovery ancillas. In the last chapter quantum error protection methods, decoherence-free subspaces and subsystems, are studied in the framework of linear maps. This framework provides the most general description of open quantum system dynamics.

Taghavi, Soraya

191

Quantum error correcting codes and one-way quantum computing: Towards a quantum memory

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 conc...

Schlingemann, Dirk

2003-01-01

192

Experimental Demonstration of Quantum Lattice Gas Computation

We report an ensemble nuclear magnetic resonance (NMR) implementation of a quantum lattice gas algorithm for the diffusion equation. The algorithm employs an array of quantum information processors sharing classical information, a novel architecture referred to as a type-II quantum computer. This concrete implementation provides a test example from which to probe the strengths and limitations of this new computation paradigm. The NMR experiment consists of encoding a mass density onto an array of 16 two-qubit quantum information processors and then following the computation through 7 time steps of the algorithm. The results show good agreement with the analytic solution for diffusive dynamics. We also describe numerical simulations of the NMR implementation. The simulations aid in determining sources of experimental errors, and they help define the limits of the implementation.

Pravia, M A; Yepez, J; Cory, D G; Pravia, Marco A.; Chen, Zhiying; Yepez, Jeffrey; Cory, David G.

2003-01-01

193

Prospects for quantum computing: Extremely doubtful

The quantum computer is supposed to process information by applying unitary transformations to 2N complex amplitudes defining the state of N qubits. A useful machine needing N 103 or more, the number of continuous parameters describing the state of a quantum computer at any given moment is at least 21000 10300 which is much greater than the number of protons in the Universe. However, the theorists believe that the feasibility of large-scale quantum computing has been proved via the “threshold theorem”. Like for any theorem, the proof is based on a number of assumptions considered as axioms. However, in the physical world none of these assumptions can be fulfilled exactly. Any assumption can be only approached with some limited precision. So, the rather meaningless “error per qubit per gate” threshold must be supplemented by a list of the precisions with which all assumptions behind the threshold theorem should hold. Such a list still does not exist. The theory also seems to ignore the undesired free evolution of the quantum computer caused by the energy differences of quantum states entering any given superposition. Another important point is that the hypothetical quantum computer will be a system of 103 -106 qubits PLUS an extremely complex and monstrously sophisticated classical apparatus. This huge and strongly nonlinear system will generally exhibit instabilities and chaotic behavior.

Dyakonov, M. I.

2014-09-01

194

Quantum-cellular-automata quantum computing with endohedral fullerenes

International Nuclear Information System (INIS)

We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of group-V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state S=3/2. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automaton is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum-cellular-automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automaton operation and obtain a rough figure of merit for the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes toward meeting the fifth criterion: qubit readout

195

The pre-history of quantum computation

The main ideas behind developments in the theory and technology of quantum computation were formulated in the late 1970s and early 1980s by two physicists in the West and a mathematician in the former Soviet Union. It is not generally known in the West that the subject has roots in the Russian technical literature. The author hopes to present as impartial a synthesis as possible of the early history of thought on this subject. The role of reversible and irreversible computational processes is examined briefly as it relates to the origins of quantum computing and the so-called Information Paradox in physics.

Potgieter, P H

2004-01-01

196

Quantum Computing in Solid State, and Coherent Behavior of Open Quantum Systems.

We have developed and investigated models of realization of quantum computing in solid-state semiconductor heterostructures, and explored decoherence properties of relevance in evaluation of quantum-computing systems. Quantum bits (qubits) are nuclear or ...

V. Privman

2003-01-01

197

Quantum computation with un-tunable couplings

Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme to remove the necessity of switching the couplings between qubits for two bit gates, which are more costly in many cases. Our strategy is to compute in and out of carefully designed interaction free subspaces analogous to decoherence free subspaces, which allows us to effectively turn off and turn on the interactions between the encoded qubits. We give two examples to show how universal quantum computation is realized in our scheme with local manipulations to physical qubits only, for both diagonal and off diagonal interactions.

Zhou, X; Guo, G C; Feldman, M J; Zhou, Xingxiang; Zhou, Zheng-Wei; Guo, Guang-Can; Feldman, Marc J.

2002-01-01

198

Quantum Computers: A New Paradigm in Information Technology

Digital Repository Infrastructure Vision for European Research (DRIVER)

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, i...

Raisinghani, Mahesh S.

2001-01-01

199

Information-theoretic temporal Bell inequality and quantum computation

International Nuclear Information System (INIS)

An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation

200

Recipes for spin-based quantum computing

Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics. Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer. In thi...

Cerletti, V; Gywat, O; Loss, D; Cerletti, Veronica; Gywat, Oliver; Loss, Daniel

2005-01-01

201

Analogue Quantum Computers for Data Analysis

Digital Repository Infrastructure Vision for European Research (DRIVER)

Analogue computers use continuous properties of physical system for modeling. In the paper is described possibility of modeling by analogue quantum computers for some model of data analysis. It is analogue associative memory and a formal neural network. A particularity of the models is combination of continuous internal processes with discrete set of output states. The modeling of the system by classical analogue computers was offered long times ago, but now it is not very e...

Vlasov, Alexander Yu

1998-01-01

202

Simulated Quantum Computation of Global Minima

Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations $N$ reduced from O(N) in classical simulation to $O(\\sqrt{N})$ in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimization to treat larger systems.

Zhu, Jing; Kais, Sabre

2009-01-01

203

Optical quantum computer based on RDS crystal

Digital Repository Infrastructure Vision for European Research (DRIVER)

We have proposed the construction of optical quantum computer (OQC) on regular domain structure (RDS) crystal. By using RDS crystal, we can perform all the logical operations on one RDS crystal. Moreover, RDS crystals are parctically independent to the heating effects i.e., can perform logic operations constantly without cooling the RDS crystal. Also, we have proposed the quantum parallelsim i.e., parallel coherent laser beams are injected at the input of the RDS crystals. B...

Sazonova, Z. S.; Singh, Ranjit

2001-01-01

204

Local Search Methods for Quantum Computers

Digital Repository Infrastructure Vision for European Research (DRIVER)

Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An example of such a local quantum search is evaluated empirically for the satisfiability (SAT) problem and shown to be particularly effective for highly constrained instances. For problems with an intermediate number of constraints, it is som...

Hogg, Tad; Yanik, Mehmet

1998-01-01

205

Verification for measurement-only blind quantum computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

Blind quantum computing is a new secure quantum computing protocol where a client who does not have any sophisticated quantum technlogy can delegate her quantum computing to a server without leaking any privacy. It is known that a client who has only a measurement device can perform blind quantum computing [T. Morimae and K. Fujii, Phys. Rev. A {\\bf87}, 050301(R) (2013)]. It has been an open problem whether the protocol can enjoy the verification, i.e., the ability of client...

Morimae, Tomoyuki

2012-01-01

206

Universal dephasing control during quantum computation

International Nuclear Information System (INIS)

Dephasing is a ubiquitous phenomenon that leads to the loss of coherence in quantum systems and the corruption of quantum information. We present a universal dynamical control approach to combat dephasing during all stages of quantum computation, namely, storage and single- and two-qubit operators. We show that (a) tailoring multifrequency gate pulses to the dephasing dynamics can increase fidelity; (b) cross-dephasing, introduced by entanglement, can be eliminated by appropriate control fields; (c) counterintuitively and contrary to previous schemes, one can increase the gate duration, while simultaneously increasing the total gate fidelity

207

Quantum Computation of Scattering in Scalar Quantum Field Theories

Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.

Jordan, Stephen P; Preskill, John

2011-01-01

208

Quantum Computation and Quantum Measurements with Mesoscopic Superconducting Structures

Systems of mesoscopic Josephson junctions are at present among the leading candidates for development of practical qubits for quantum information devices. Although different qubit structures have been realized with Josephson junctions, their common feature is the design that is optimized to overcome the problem of decoherence by the low-frequency noise that exists in all solid-state structures. In the presented dissertation research, we propose and study an alternative approach of direct suppression of noise by a feedback loop based on the low-frequency quantum measurements. The minimal noise induced in the qubit by such a feedback loop is calculated under the conditions of continuous quantum-limited measurements. Another obstacle facing the quantum Josephson junction circuits is the information transfer between the circuit elements. Here we study the quantum dynamics of dual-rail arrays of nSQUIDs characterized by a negative inductance between its arms, which hold promise for quantum information transfer. The scaling and decoherence properties of these arrays are analyzed. Information transfer along nSQUID arrays can also be used to implement adiabatic quantum computation (AQC), an alternative to the gate-model approach to quantum computation that is expected to be more stable against the decoherence. Here we suggest fidelity of the ground state as the quantitative measure of the ultimate effect of decoherence on AQC. We show that decoherence-induced deformation of the ground state of an AQC algorithm is characterized by the same noise correlators as those that determine the decoherence time in the gate-model approach. Results for fidelity of a 16-qubit array at finite temperatures are obtained numerically.

Deng, Qiang

209

Digital Repository Infrastructure Vision for European Research (DRIVER)

The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and it has been used to compute the capacity of quant um channel for quantum comm...

Ohya, Masanori

1998-01-01

210

Symmetry, Reversibility and Efficiency of Quantum Computation

The reason for the higher efficiency exhibited by some quantum algorithms over their classical counterparts is examined by considering the interplay between the reversible actions required to prepare the computer registers in an entangled state before measurement (the "initial actions"), and the final measurement action -- whereas measurement is interpreted in a new way, particularly suited to a problem solving context. This unification shows that the computation process, comprising the measurement outcome, is significantly influenced by both the initial actions and the need to satisfy the constraints set by the final measurement action. Reviewing the existing quantum algorithms in the light of this dual influence, yields new valuable insight in the nature of the quantum computation speed up.

Castagnoli, G C; Sergienko, A V; Castagnoli, Giuseppe; Monti, Dalida; Sergienko, Alexander

1999-01-01

211

Methodological testing: Are fast quantum computers illusions?

Energy Technology Data Exchange (ETDEWEB)

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.

Meyer, Steven [Tachyon Design Automation, San Francisco, CA (United States)

2013-07-01

212

Processor core model for quantum computing.

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. PMID:16803291

Yung, Man-Hong; Benjamin, Simon C; Bose, Sougato

2006-06-01

213

Digital Repository Infrastructure Vision for European Research (DRIVER)

Ground-state quantum computers mimic quantum mechanical time evolution within the amplitudes of a time-independent quantum state. We explore the principles that constrain this mimicking. A no-cloning argument is found to impose strong restrictions. It is shown, however, that there is flexibility that can be exploited using quantum teleportation methods to improve ground-state quantum computer design.

Mizel, Ari

2003-01-01

214

Few electron quantum computing structures and lattice gas computation

International Nuclear Information System (INIS)

There are several paths available when downscaling devices and computing architectures to the nanoscale. The first is to keep silicon technology irrespective of computational models. In the next decade, it is clear that we have to learn to build and control devices at the nanometer and even atomic scale. These devices will use few electron quantum tunneling for state switching, wires and storage. The arena will be electron gases confined to wires or wells at milli-kelvin and even room temperatures. In this paper, the authors focus their aims on building a quantum electronics based on few electron nanodevices and quantum dot arrays. Nandoevices could initially be made with a technology that allows sufficient quantity and diversity for at least special purpose processing tasks. hopefully, one can also see how to do large scale general computation

215

From Cbits to Qbits: Teaching computer scientists quantum mechanics

In this article, a strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory.

Mermin, N. D.

2004-04-29

216

Adiabatic graph-state quantum computation

Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any MBQC on a graph state with generalized flow (gflow) can be converted into an adiabatically driven holonomic computation, which we call adiabatic graph-state quantum computation (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of \\dot{H} as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated.

Antonio, B.; Markham, D.; Anders, J.

2014-11-01

217

Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious

Digital Repository Infrastructure Vision for European Research (DRIVER)

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.

Cirasella, Jill

2009-01-01

218

Quantum game simulator, using the circuit model of quantum computation

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 0.4 sec (Region Feature) and 0.3 sec (Payoff Feature) on a Intel Core 2 Duo GHz with 2 GB of memory under Windows XP.

Vlachos, Panagiotis; Karafyllidis, Ioannis G.

2009-10-01

219

Fabrication technologies for solid state quantum computation

International Nuclear Information System (INIS)

Full text: Quantum computers exploit the superposition and entanglement of quantum states to enable the operation of certain algorithms, such as factoring large numbers, which are not feasible on a conventional computer. A recent proposal developed at UNSW for a silicon-based nuclear spin quantum computer offers perhaps the best opportunity for a practical and scalable quantum processor. These devices will require placement, with atomic precision, of 31P dopants within isotopically-pure 28Si, and the subsequent deposition of nanoscale metal gates on the surface, registered to the donors. We will present strategies for the fabrication of such multi-qubit devices which employ a hydrogen-on-silicon resist technology in which a scanned probe is used to perform atomic-scale lithography. Subsequent fabrication steps include epitaxial silicon growth and electron-beam lithography. In these devices quantum information is encoded on the spins of the 31P nuclei and can be transferred to the donor electrons via the hyperfine interaction. We describe how an Al/Al2O3 single-electron transistor can be used to detect the spin of individual electrons, thereby indirectly achieving nuclear spin readout

220

Another Look at Quantum Neural Computing

The term quantum neural computing was coined to indicate a unity in the functioning of the brain. We revisit the concept and also summarize new arguments related to the learning modes of the brain in response to sensory input that may be aggregated in three types: associative, reorganizational, and quantum. The associative and reorganizational types are quite apparent based on experimental findings; it is much harder to establish that the brain as an entity exhibits quantum properties. We argue that the reorganizational behavior of the brain may be viewed as inner adjustment corresponding to its quantum behavior at the system level. Not only neural structures but their higher abstractions also may be seen as whole entities. We consider the dualities associated with the behavior of the brain and how these dualities are bridged.

Kak, Subhash

2009-01-01

221

Temporal resources for global quantum computing architectures

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: English Abstract in english Using the methods for optimal simulation of quantum logic gates, we perform a quantitative estimation of the time resources involved in the execution of universal gate sets for the case of three representative models of quantum computation based on global control. The importance of such models stems [...] from the solution to the problem of experimentally addressing and locally manipulating the qubits in a given quantum register. The numerical estimation of the temporal efficiency for each model is performed by assuming that the qubits in the register can be coupled to each other via the Ising and the Förster interactions. Finally, we discuss the feasibility of the physical realization of such architectures under quantum error correction conditions.

Juan D., Jaramillo; John H., Reina.

2008-12-01

222

Quantum Computation, Complexity, and Many-Body Physics

Digital Repository Infrastructure Vision for European Research (DRIVER)

Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating non-classical correlations, or quantum entanglement, which is a phenomena hard or impossible to reproduce by classical-information methods. In this thesis I first investigate the simulation of quantum systems on a quantum computer constructed of...

Somma, Rolando D.

2005-01-01

223

Realizing universal Majorana fermionic quantum computation

Majorana fermionic quantum computation (MFQC) was proposed by S. B. Bravyi and A. Yu. Kitaev [Ann. Phys. (NY) 298, 210 (2002), 10.1006/aphy.2002.6254], who indicated that a (nontopological) fault-tolerant quantum computer built from Majorana fermions may be more efficient than that built from distinguishable two-state systems. However, until now scientists have not known how to realize a MFQC in a physical system. In this paper we propose a possible realization of MFQC. We find that the end of a line defect of a p-wave superconductor or superfluid in a honeycomb lattice traps a Majorana zero mode, which becomes the starting point of MFQC. Then we show how to manipulate Majorana fermions to perform universal MFQC, which possesses possibilities for high-level local controllability through individually addressing the quantum states of individual constituent elements by using timely cold-atom technology.

Wu, Ya-Jie; He, Jing; Kou, Su-Peng

2014-08-01

224

Universal quantum computation in a hidden basis

Suppose we are given several copies each of two orthogonal states $\\ketz$ and $\\keto$ that are promised to come from known orthogonal subspaces, but are otherwise unknown. We consider the quantum-information-theoretic tasks of state preparation and universal quantum computation with respect to the hidden basis $\\{\\ketz,e^{i \\theta}\\keto\\}^{\\otimes l}$, of an $l$-logical-qubit system, for a random $\\theta$. We give an exact algorithm for state preparation, and give an efficient approximation algorithm for universal computation. We apply our results to quantum-public-key authentication protocols, by showing that a class of digital signature schemes is insecure and giving an example of a (potentially secure) protocol based on these techniques.

Ioannou, Lawrence M

2008-01-01

225

Computing hypergraph Ramsey numbers by using quantum circuit

Gaitan and Clark (Phys Rev Lett 108:010501, 2012) have recently shown a quantum algorithm for the computation of the Ramsey numbers using adiabatic quantum evolution. We present a quantum algorithm to compute the two-color Ramsey numbers for r-uniform hypergraphs by using the quantum counting circuit.

Qu, Ri; Li, Zong-shang; Wang, Juan; Bao, Yan-ru; Cao, Xiao-chun

2013-07-01

226

Universal quantum computing based on monodromy representations

Digital Repository Infrastructure Vision for European Research (DRIVER)

A model of quantum computing is presented, based on properties of connections with a prescribed monodromy group on holomorphic vector bundles over bases with nontrivial topology. Such connections with required properties appear in the WZW-models, in which moreover the corresponding n-point correlation functions are sections of appropriate bundles which are holomorphic with respect to the connection.

Giorgadze, Gia

2002-01-01

227

Interactive Quantum Mechanics Quantum Experiments on the Computer

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...

Brandt, S; Dahmen, H.D

2011-01-01

228

Quantum computation with nuclear spins in quantum dots

International Nuclear Information System (INIS)

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 ensemble can be utilized for the important task of sequentially generating entanglement between electrons. This is true despite the fact that electrons and nuclei become only very weakly entangled through the hyperfine interaction. Straightforward experimentally feasible protocols for the generation of multipartite entangled (GHZ- and W-)states are presented. (orig.)

229

Quantum computation with nuclear spins in quantum dots

Energy Technology Data Exchange (ETDEWEB)

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 ensemble can be utilized for the important task of sequentially generating entanglement between electrons. This is true despite the fact that electrons and nuclei become only very weakly entangled through the hyperfine interaction. Straightforward experimentally feasible protocols for the generation of multipartite entangled (GHZ- and W-)states are presented. (orig.)

Christ, H.

2008-01-24

230

Quantum Computing: Theoretical versus Practical Possibility

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...

Paraoanu, G S

2011-01-01

231

Measurement-Based Interference in Quantum Computation

International Nuclear Information System (INIS)

The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent with the visibility in qubit systems. By taking cluster states as examples, we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits. We also find that the interference increases with the number of the computing steps. So we conjecture that the interference may be the source of the speedup of the one-way quantum computation. (general)

232

Design constraints for nanometer scale quantum computers

Nanometer scale electronics present a challenge for the computer architect. These quantum devices have small gain and are difficult to interconnect. I have analyzed current device capabilities and explored two general design requirements for the design of computers: error correction and long range connections. These two principles follow when Turing machines are implemented as integrated circuits. I consider the roles of electromigration through thin wires, circuit layout, and error rates for devices with small gain. The analysis brings into sharp focus the future of nanocomputers and suggests solutions to some of its difficulties. It gives a theoretical model for a nanocomputer, separating the roles of devices and algorithms. Within the model one can implement a stochastic computer, which operates despite quantum device limitations.

Mainieri, R

1994-01-01

233

Rapid Data Search using Adiabatic Quantum Computation

We show that by a suitable choice of time-dependent Hamiltonian, the search for a marked item in an unstructured database can be achieved in unit time, using Adiabatic Quantum Computation. This is a considerable improvement over the O(sqrt(N)) time required in previous algorithms. The trade-off is that in the intermediate stages of the computation process, the ground state energy of the computer increases to a maximum of O(sqrt(N)), before returning to zero at the end of the process.

Ahrensmeier, D; Kobes, R L; Kunstatter, G; Zaraket, H; Ahrensmeier, Daria; Das, Saurya; Kobes, Randy; Kunstatter, Gabor; Zaraket, Haitham

2002-01-01

234

QCWAVE, a Mathematica quantum computer simulation update

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...

Tabakin, Frank

2011-01-01

235

Mathematical optics classical, quantum, and computational methods

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical wave

Lakshminarayanan, Vasudevan

2012-01-01

236

Optical quantum computer based on RDS crystal

We have proposed the construction of optical quantum computer (OQC) on regular domain structure (RDS) crystal. By using RDS crystal, we can perform all the logical operations on one RDS crystal. Moreover, RDS crystals are parctically independent to the heating effects i.e., can perform logic operations constantly without cooling the RDS crystal. Also, we have proposed the quantum parallelsim i.e., parallel coherent laser beams are injected at the input of the RDS crystals. By using the RDS crystal we can perform the reduce the requirements of the linear and nonlinear optical components.

Sazonova, Z S; Singh, Ranjit

2001-01-01

237

Adiabatic cluster-state quantum computing

Models of quantum computation (QC) are important because they change the physical requirements for achieving universal QC. For example, one-way QC requires the preparation of an entangled “cluster” state, followed by adaptive measurement on this state, a set of requirements which is different from the standard quantum-circuit model. Here we introduce a model based on one-way QC but without measurements (except for the final readout), instead using adiabatic deformation of a Hamiltonian whose initial ground state is the cluster state. Our results could help increase the feasibility of adiabatic schemes by using tools from one-way QC.

Bacon, Dave; Flammia, Steven T.

2010-09-01

238

Towards Large-Scale Quantum Computation

This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout gates, followed by linear nearest neighbor implementations of 5-qubit quantum error correction with and without fast measurement. A linear nearest neighbor circuit implementing Shor's algorithm is presented, then modified to remove the need for exponentially small rotation gates. Finally, a method of constructing optimal approximations of arbitrary single-qubit fault-tolerant gates is described and applied to the specific case of the remaining rotation gates required by Shor's algorithm.

Fowler, A G

2005-01-01

239

Qutrit quantum computer with trapped ions

International Nuclear Information System (INIS)

We study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits

240

Efficiency of open quantum walk implementation of dissipative quantum computing algorithms

Digital Repository Infrastructure Vision for European Research (DRIVER)

An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on the open quantum walk formalism are more efficient than the canonical dissipative quantum computing approach. In particular, the open quantum walks can be designed to converge faster to the desired steady state and to increase the probabil...

Sinayskiy, I.; Petruccione, F.

2014-01-01

241

A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 M...

Lomonaco, Samuel J.; jr

2000-01-01

242

Realizing the quantum baker's map on a 3-qubit NMR quantum computer

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.

Brun, T A; Brun, Todd A.; Schack, Ruediger

1999-01-01

243

Qdensity - a Mathematica Quantum Computer Simulation

This Mathematica 5.2 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 {\\it Qdensity.m} which contains the tools needed in quantum circuits, e.g. multiqubit kets, projectors, gates, etc. A tutorial notebook, {\\it Tutorial.nb} is provided that serves as a guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: {\\it QFT.nb}, {\\it Teleportation.nb}, {\\it Grover.nb} and {\\it Shor.nb} where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of "one way computing" ideas, are included as an additional tool in the notebook {\\i...

Juliá-Diaz, B

2005-01-01

244

Buckyball quantum computer: realization of a quantum gate

We have studied a system composed by two endohedral fullerene molecules. We have found that this system can be used as good candidate for the realization of quantum gates. Each of these molecules encapsules an atom carrying a spin, therefore they interact through the spin dipole interaction. We show that a phase gate can be realized if we apply static and time dependent magnetic fields on each encased spin. We have evaluated the operational time of a ?-phase gate, which is of the order of ns. We made a comparison between the theoretical estimation of the gate time and the experimental decoherence time for each spin. The comparison shows that the spin relaxation time is much larger than the ?-gate operational time. Therefore, this indicates that, during the decoherence time, it is possible to perform some thousands of quantum computational operations. Moreover, through the study of concurrence, we get very good results for the entanglement degree of the two-qubit system. This finding opens a new avenue for the realization of quantum computers.

Garelli, M. S.; Kusmartsev, F. V.

2005-11-01

245

Period finding with adiabatic quantum computation

We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the “period”, or xor mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its theoretical and experimental implications for the existence of an adiabatic version of Shor's integer factorization algorithm that would have the same complexity as the original algorithm.

Hen, I.

2014-03-01

246

Quantum computation architecture using optical tweezers

International Nuclear Information System (INIS)

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 require the transport of atoms to neighboring sites. We numerically optimize the nonadiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few 100 ?s, while keeping the error probability due to vibrational excitations and spontaneous scattering below 10-3. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing.

247

Brain-Computer Interfaces and Quantum Robots

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 occurrenc...

Pessa, Eliano; Zizzi, Paola

2009-01-01

248

Towards Lagrangian approach to quantum computations (revised)

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 t...

Vlasov, Alexander Yu

2003-01-01

249

Testing pairing models on a quantum computer

We propose an explicit algorithm for efficient simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm finds the low-lying spectrum in the vicinity of the gap between ground and first excited states, and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultrasmall metallic grains.

Wu, L A; Lidar, D A

2002-01-01

250

Adiabatic Quantum Computation in Open Systems

Digital Repository Infrastructure Vision for European Research (DRIVER)

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between ...

Sarandy, M. S.; Lidar, D. A.

2005-01-01

251

Data Structures in Classical and Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

This survey summarizes several results about quantum computing related to (mostly static) data structures. First, we describe classical data structures for the set membership and the predecessor search problems: Perfect Hash tables for set membership by Fredman, Koml\\'{o}s and Szemer\\'{e}di and a data structure by Beame and Fich for predecessor search. We also prove results about their space complexity (how many bits are required) and time complexity (how many bits have to b...

Fillinger, Maximilian

2013-01-01

252

The power of noisy fermionic quantum computation

International Nuclear Information System (INIS)

We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi (2006 Phys. Rev. A 73 042313) that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular four-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in this region, while for noise rates below 53% we prove that the state is not a mixture of Gaussian states. These results are obtained by generalizing concepts in entanglement theory to the setting of Gaussian states and their convex mixtures. In particular, we develop a complete set of criteria, namely the existence of a Gaussian-symmetric extension, which determine whether a state is a convex mixture of Gaussian states. (paper)

253

Quantum Cellular Automata: Computing with Quantum Dot Molecules

A new quantum computing architecture, quantum cellular automata, is studied. Quantum cellular automata (QCA's) are composed of interacting quantum dot molecules, each of which contains two electrons. Repulsion between these two electrons causes these molecules to exhibit bistable behavior, which allows the encoding of binary information directly in the quantum state of each cell. QCA's take advantage of "computing with the ground state", in which dissipation acts to drive the system to the ground state corresponding to the applied boundary conditions. By carefully designing the geometric layout of arrays of these quantum dot molecules, it is possible to perform useful calculations with these ground state alignments. The logic primitive of such a system is a majority logic gate, which can be reduced to act as either an AND gate or an OR gate. Due to the local nature of the Coulombic interaction between cells, it is possible to use hierarchical design rules to combine these elements into more complicated logic devices. Since the interactions between cells are purely Coulombic, no direct interconnections are necessary between QCA cells. In addition, energy is only supplied at the edge of the system when an input cell is switched, so QCA's can be said to be truly edge-driven. Such an edge-driven system will eliminate many of the fabrication challenges present in systems with complicated interconnection requirements. Although the results of a ground-state calculation do not rely on the exact nature of the system dynamics, these dynamics do provide an estimate of the switching speed of QCA devices. We have developed several approximate techniques for the modeling of this very complicated system and have obtained estimates on the intrinsic switching speed of both semiconductor-based cells and macro-molecular cells. As expected, the macro-molecular cells exhibit greatly improved performance over the larger semiconductor cells. An alternative to abrupt switching of QCA arrays takes advantage of the adiabatic theorem to guarantee that the system will always remain in its instantaneous ground state. Such adiabatic switching has several advantages over abrupt switching, the most important of which is avoidance of metastable states.

Tougaw, Paul Douglas

254

PREFACE: Quantum Information, Communication, Computation and Cryptography

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 systems, the second by T Prosen, discussing chaos and complexity in quantum systems. Both topics have theoretical as well as experimental relevance and are likely to witness a fast growing development in the near future. The remaining contributions present more specific and very recent results. They involve the study of the structure of quantum states and their estimation (B Baumgartner et al, C King et al, S Olivares et al, D Petz et al and W van Dam et al), of entanglement generation and its quantification (G Brida et al, F Ciccarello et al, G Costantini et al, O Romero-Isart et al, D Rossini et al, A Serafini et al and D Vitali et al), of randomness related effects on entanglement behaviour (I Akhalwaya et al, O Dahlsten et al and L Viola et al), and of abstract and applied aspects of quantum computation and communication (K Audenart, G M D'Ariano et al, N Datta et al, L C Kwek et al and M Nathanson et al). We would like to express our gratitude to the European Commission, the Abdus Salam ICTP, SISSA and Eurotech SpA (Amaro, Udine, Italy) for financial and/or logistic support. Special thanks also go to the workshop secretary Marina De Comelli, and the secretaries of the Department of Theoretical Physics, University of Trieste, Sabrina Gaspardis and Rosita Glavina for their precious help and assistance.

Benatti, F.; Fannes, M.; Floreanini, R.; Petritis, D.

2007-07-01

255

An Introduction to Quantum Computing using Cavity QED concepts

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a concise but complete conceptual treatment of quantum computing implemented with Cavity Quantum Electrodynamics (CQED. The paper is intended as a brief overview for professionals who are coming over to the field from other areas and who may have not discussed the concepts behind quantum computing during their technical training.

Burell, Zachary

2012-01-01

256

Nonadiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Xu, G. F.; Zhang, J.; Tong, D. M.; Sjöqvist, Erik; Kwek, L. C.

2012-10-01

257

Hybrid architecture for encoded measurement-based quantum computation.

We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within the considered error model a threshold of the order of 10% local noise per particle for fault-tolerant quantum computation and quantum communication. PMID:24946906

Zwerger, M; Briegel, H J; Dür, W

2014-01-01

258

Universal Quantum Computing with Spin and Valley

We investigate a two-electron double quantum dot with both spin and valley degrees of freedom as they occur in graphene, carbon nanotubes, or silicon, and regard the 16-dimensional space with one electron per dot as a four-qubit logic space. In the spin-only case, it is well known that the exchange coupling between the dots combined with arbitrary single-qubit operations is sufficient for universal quantum computation. The presence of the valley degeneracy in the electronic band structure alters the form of the exchange coupling and in general leads to spin-valley entanglement. Here, we show that universal quantum computation can still be performed by exchange interaction and single-qubit gates in the presence of the additional (valley) degree of freedom. We present an explicit pulse sequence for a spin-only controlled-NOT consisting of the generalized exchange coupling and single-electron spin and valley rotations. We also propose state preparations and projective measurements with the use of adiabatic trans...

Rohling, Niklas

2012-01-01

259

Quantum computation over the butterfly network

International Nuclear Information System (INIS)

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

260

Robust logic gates and realistic quantum computation

International Nuclear Information System (INIS)

The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on the BB1 family of composite rotations have been experimentally demonstrated in a variety of systems, but little study has been made of their application in extended computations, and there has been no experimental study of the corresponding robust two qubit gates to date. Here we describe an application of robust gates to nuclear magnetic resonance studies of approximate quantum counting. We find that the BB1 family of robust gates is indeed useful, but that the related NB1, PB1, B4, and P4 families of tailored logic gates are less useful than initially expected

261

QCWAVE - A Mathematica quantum computer simulation update

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 (2×2, 4×4 or 8×8) matrices acting on the 2 amplitudes for a system of nq 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 multiverse approach, as described in our QCMPI paper. This multiverse approach involves using the present slave-master parallel processing capabilities of Mathematica 7.0/8.0 to simulate errors and error correction. The basic idea is that parallel versions of QCWAVE run simultaneously with random errors introduced on some of the processors, with an ensemble average used to represent the real world situation. Within this approach, error correction steps can be simulated and their efficacy tested. This capability allows one to examine the detrimental effects of errors and the benefits of error correction on particular quantum algorithms. Other upgrades provided in this version include circuit-diagram drawing commands, better Dirac form and amplitude display features. These are included in the add-ons QCWave.m and Circuits.m, and are illustrated in tutorial notebooks. In separate notebooks, QCWAVE is applied to sample algorithms in which the parallel multiverse setup is illustrated and error correction is simulated. These extensions and upgrades will hopefully help in both instruction and in application to QC dynamics and error correction studies.

Tabakin, Frank; Juliá-Díaz, Bruno

2011-08-01

262

Energy Technology Data Exchange (ETDEWEB)

I will discuss the revolutionary new concept of topological quantum computation, which is fault-tolerant at the hardware level with no need, in principle, of any quantum error correction protocols. Errors simply do not occur since the physical qubits and the computation steps are protected against decoherence by non-local topological correlations in the underlying physical system. The key idea is non-Abelian statistics of the quasiparticles (called 'anyons' as opposed to fermions or bosons), where the space-time braiding of the anyons around each other, i.e. quantum 'knots', form topologically protected quantum gate operations. I will describe in detail the theoretical principles guiding the experimental search for the appropriate topological phases of matter where such non-Abelian anyons, which are low-dimensional solid state versions of the elusive and exotic Majorana fermions hypothesized seventy-five years ago, may exist. I will critically discuss the recent experimental claims of observing the Majorana modes in semiconductor nanowire structures following earlier theoretical proposals, outlining the future developments which would be necessary to eventually build a topological quantum computer.

Das Sarma, Sankar [University of Maryland

2012-10-03

263

Quantum Computing, $NP$-complete Problems and Chaotic Dynamics

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.

Ohya, M; Ohya, Masanori; Volovich, Igor V.

1999-01-01

264

Quantum Computation: Particle and Wave Aspects of Algorithms

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.

Patel, Apoorva

2011-01-01

265

Quantum computing in a macroscopic dark period

International Nuclear Information System (INIS)

Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one- and two-bit gate operations. How this works can be understood by comparing the system with a three-level atom exhibiting a macroscopic dark period. In addition, a dynamical explanation is given for a scheme based on atoms inside an optical cavity in the strong-coupling regime and we show how spontaneous emission by the atoms can be highly suppressed

266

Adiabatic quantum computation in open systems

We analyze the performance of the adiabatic quantum computation (AQC) paradigm under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to the analysis based on the adiabatic theorem for closed systems, we show that a system may initially be in an adiabatic regime, but then transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria. As an illustrative example, we analyze the adiabatic implementation of the Deutsch-Jozsa algorithm under dephasing.

Sarandy, M S

2005-01-01

267

Spintronics and Quantum Computing Switching Mechanisms for Qubits

Quantum computing and quantum communication are remarkable examples of new information processing technologies that arise from the coherent manipulation of spins in nanostructures. We review our theoretical proposal for using electron spins in quantum-confined nanostructures as qubits. We present single- and two-qubit gate mechanisms in laterally as well as vertically coupled quantum dots and discuss the possibility to couple spins in quantum dots via exchange or superexchange. In addition, we propose a new stationary wave switch, which allows to perform quantum operations with quantum dots or spin-1/2 molecules placed on a 1D or 2D lattice.

Leuenberger, M N; Leuenberger, Michael N.; Loss, Daniel

2000-01-01

268

Quantum computing accelerator I/O : LDRD 52750 final report.

Energy Technology Data Exchange (ETDEWEB)

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 proposed as a result of this work.

Schroeppel, Richard Crabtree; Modine, Normand Arthur; Ganti, Anand; Pierson, Lyndon George; Tigges, Christopher P.

2003-12-01

269

Quantum computing accelerator I/O : LDRD 52750 final report

International Nuclear Information System (INIS)

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 proposed as a result of this work

270

Globally controlled artificial semiconducting molecules as quantum computers

Digital Repository Infrastructure Vision for European Research (DRIVER)

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...

Tribollet, Jerome

2005-01-01

271

Lecture Script: Introduction to Computational Quantum Mechanics

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...

Schmied, Roman

2014-01-01

272

Tomography and spectroscopy as quantum computations

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...

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

273

QDENSITY—A Mathematica Quantum Computer simulation

This Mathematica 5.2 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. Selected examples of the basic commands are presented here and a tutorial notebook, Tutorial.nb is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: QFT.nb, Teleportation.nb, Grover.nb and Shor.nb where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of "one way computing" ideas, are included as an additional tool in the notebook Cluster.nb. A Mathematica palette containing most commands in QDENSITY is also included: QDENSpalette.nb. Program summaryTitle of program: QDENSITY Catalogue identifier: ADXH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v1_0 Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating systems: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4 Programming language used: Mathematica 5.2 No. of bytes in distributed program, including test data, etc.: 180 581 No. of lines in distributed program, including test data, etc.: 19 382 Distribution format: tar.gz Method of solution: 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. QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY.

Juliá-Díaz, Bruno; Burdis, Joseph M.; Tabakin, Frank

2006-06-01

274

Surface code quantum computing by lattice surgery

In recent years, surface codes have become the preferred method for quantum error correction in large scale computational and communications architectures. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfa...

Horsman, Clare; Devitt, Simon; Van Meter, Rodney

2011-01-01

275

Measurement-only topological quantum computation via anyonic interferometry

International Nuclear Information System (INIS)

We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using 'forced measurement' protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems

276

Measurement-Only Topological Quantum Computation via Anyonic Interferometry

We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using "forced measurement" protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.

Bonderson, Parsa; Nayak, Chetan

2008-01-01

277

Transitions in the computational power of thermal states for measurement-based quantum computation

The quantum state of a many-body system can serve as a resource for a method of quantum computing based solely on adaptive local measurements. We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition in the underlying model; indeed this model does not possess any phase transitions, classical or quantum.

Barrett, Sean D; Doherty, Andrew C; Jennings, David; Rudolph, Terry

2008-01-01

278

Buckyball Quantum Computer: Realization of a Quantum Gate

We have studied a system composed by two endohedral fullerene molecules. We have found that this system can be used as good candidate for the realization of Quantum Gates Each of these molecules encapsules an atom carrying a spin,therefore they interact through the spin dipole interaction. We show that a phase gate can be realized if we apply on each encased spin static and time dependent magnetic field. We have evaluated the operational time of a $\\pi$-phase gate, which is of the order of ns. We made a comparison between the theoretical estimation of the gate time and the experimental decoherence time for each spin. The comparison shows that the spin relaxation time is much larger than the $\\pi$-gate operational time. Therefore, this indicates that, during the decoherence time, it is possible to perform some thousands of quantum computational operations. Moreover, through the study of concurrence, we get very good results for the entanglement degree of the two-qubit system. This finding opens a new avenue fo...

Garelli, M S

2005-01-01

279

Multiple network alignment on quantum computers

Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large biomolecules, and recurring patterns of interactions in social networks. A large class of such analyses methods quantify the topological similarity of nodes across networks. The resulting correspondence of nodes across networks, also called node alignment, can be used to identify invariant subgraphs across the input graphs. Given $k$ graphs as input, alignment algorithms use topological information to assign a similarity score to each $k$-tuple of nodes, with elements (nodes) drawn from each of the input graphs. Nodes are considered similar if their neighbors are also similar. An alternate, equivalent view of these network alignment algorithms is to consider the Kronecker product of the input graphs, and to identify high-ranked nodes in the Kronecker product graph. Conventional methods such as PageRank and HITS (Hypertext Induced Topic Selection) can be used for this purpose. These methods typically require computation of the principal eigenvector of a suitably modified Kronecker product matrix of the input graphs. We adopt this alternate view of the problem to address the problem of multiple network alignment. Using the phase estimation algorithm, we show that the multiple network alignment problem can be efficiently solved on quantum computers. We characterize the accuracy and performance of our method, and show that it can deliver exponential speedups over conventional (non-quantum) methods.

Daskin, Anmer; Grama, Ananth; Kais, Sabre

2014-09-01

280

Clifford quantum computer and the Mathieu groups

One learned from Gottesman-Knill theorem that the Clifford model of quantum computing \\cite{Clark07} may be generated from a few quantum gates, the Hadamard, Phase and Controlled-Z gates, and efficiently simulated on a classical computer. We employ the group theoretical package GAP\\cite{GAP} for simulating the two qubit Clifford group $\\mathcal{C}_2$. We already found that the symmetric group S(6), aka the automorphism group of the generalized quadrangle W(2), controls the geometry of the two-qubit Pauli graph \\cite{Pauligraphs}. Now we find that the {\\it inner} group ${Inn}(\\mathcal{C}_2)=\\mathcal{C}_2/{Center}(\\mathcal{C}_2)$ exactly contains two normal subgroups, one isomorphic to $\\mathcal{Z}_2^{\\times 4}$ (of order 16), and the second isomorphic to the parent $A'(6)$ (of order 5760) of the alternating group A(6). The group $A'(6)$ stabilizes an {\\it hexad} in the Steiner system $S(3,6,22)$ attached to the Mathieu group M(22). Both groups A(6) and $A'(6)$ have an {\\it outer} automorphism group $\\mathcal{Z...

Planat, Michel

2007-01-01

281

A Blueprint for a Topologically Fault-tolerant Quantum Computer

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...

Bonderson, Parsa; Freedman, Michael; Nayak, Chetan

2010-01-01

282

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

Digital Repository Infrastructure Vision for European Research (DRIVER)

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical...

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

2010-01-01

283

An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation

Digital Repository Infrastructure Vision for European Research (DRIVER)

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-cor...

Gottesman, Daniel

2009-01-01

284

Quantum computation and the evaluation of tensor networks

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. We use this algorithm to derive new quantum algorithms that approximate the partition function of a variety of classical statistical mechanics models, including the Potts model.

Arad, Itai

2008-01-01

285

Preparing Projected Entangled Pair States on a Quantum Computer

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.

Schwarz, Martin; Temme, Kristan; Verstraete, Frank

2012-03-01

286

Preparing projected entangled pair states on a quantum computer

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a quantum algorithm to prepare injective 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' parent Hamiltonian.

Schwarz, Martin; Temme, Kristan; Verstraete, Frank

2011-01-01

287

Consequences and Limitations of Conventional Computers and their Solutions through Quantum Computers

Directory of Open Access Journals (Sweden)

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.

Sanjaykumar DALVI

2011-12-01

288

Quantum computing based on space states without charge transfer

International Nuclear Information System (INIS)

An implementation of a quantum computer based on space states in double quantum dots is discussed. There is no charge transfer in qubits during a calculation, therefore, uncontrolled entanglement between qubits due to long-range Coulomb interaction is suppressed. Encoding and processing of quantum information is merely performed on symmetric and antisymmetric states of the electron in double quantum dots. Other plausible sources of decoherence caused by interaction with phonons and gates could be substantially suppressed in the structure as well. We also demonstrate how all necessary quantum logic operations, initialization, writing, and read-out could be carried out in the computer.

289

Algebras and universal quantum computations with higher dimensional systems

Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and discussed well known applications to product operator formalism in NMR, Jordan-Wigner construction in fermionic quantum computations. It is introduced universal set of quantum gates for higher dimensional system (``qudit''), as some generalization of these models. Finally it is briefly mentioned possible application of such algebraic methods to design of quantum processors (programmable gates arrays) and discussed generalization to quantum computation with continuous variables.

Vlasov, A Yu

2002-01-01

290

Practical experimental certification of computational quantum gates via twirling

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...

Moussa, Osama; Ryan, Colm A; Laflamme, Raymond

2011-01-01

291

From transistor to trapped-ion computers for quantum chemistry

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.

Yung, M.-H.; Casanova, J.; Mezzacapo, A.; McClean, J.; Lamata, L.; Aspuru-Guzik, A.; Solano, E.

2014-01-01

292

Knot Logic and Topological Quantum Computing with Majorana Fermions

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper is an introduction to relationships between quantum topology and quantum computing. We take a foundational approach, showing how knots are related not just to braiding and quantum operators, but to quantum set theoretical foundations and algebras of fermions. We show how the operation of negation in logic, seen as both a value and an operator, can generate the fusion algebra for a Majorana fermion, a particle that is its own anti-particle and interacts with itself...

Kauffman, Louis H.

2013-01-01

293

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...

D'Ariano, Giacomo Mauro

2010-01-01

294

The Brain Is both Neurocomputer and Quantum Computer

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…

Hameroff, Stuart R.

2007-01-01

295

Cellular automata in computational quantum chemistry

Cellular Automata (CA) are discrete dynamical systems constructed from a large number of simple identical components with local interactions, which are together capable of complex self-organizing behaviour. The complexity is generated by the cooperative effect of the many components. The use of CA in molecular and solid state dynamical calculations is relatively new and untested. Such methods, however, reduce the quantum molecular problem from one of solving differential equations to the computation of simple algebraic rules synchronously on a lattice of sites. We have demonstrated that the second quantized formalism of field operators in coordinate representation is readily implementable in terms of CA collision rules on a lattice. The Su-Schrieffer-Heeger (SSH) Hamiltonian for quasi-one-dimensional polymer chains has been examined in terms of CA rules. The CA consists of a 1-D lattice of sites, each with a finite set of possible values, representing elements of electronic charge and phonon number, evolving in discrete time steps. At each time step, the value of each site is updated according to a stochastic rule, which specifies the new value of the site in terms of its own old value and those of its nearest neighbours. The resulting CA patterns show evidence of persistent propagating structures or solitonic behaviour. In another application, a quantum mechanical variational principle is implemented as a CA, to model the approach to a stationary atomic density in Thomas-Fermi-Dirac theory.

Sukumar, N.

1995-04-01

296

Measurement-Based Quantum Computing with Valence-Bond-Solids

Digital Repository Infrastructure Vision for European Research (DRIVER)

Measurement-based quantum computing (MBQC) is a model of quantum computing that proceeds by sequential measurements of individual spins in an entangled resource state. However, it remains a challenge to produce efficiently such resource states. Would it be possible to generate these states by simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource states for MBQC, do not occur naturally as unique ground states of physical systems...

Kwek, Leong Chuan; Wei, Zhaohui; Zeng, Bei

2011-01-01

297

Possibilities of a classical alternative to a quantum computer

The dramatic increase in the efficiency of a quantum computer over a classical computer, raises a natural question asking, how much of this success could be attributed to its quantum nature and how much to its probabilistic content. To highlight this issue, we put forward the novel idea of a possible chemical computer driven by reaction-diffusion (RD) processes based on a probabilistic but classical approach. Such computers, obeying non-equilibrium statistical mechanics, can describe superpositions of empty and filled states with certain probabilities. With these {probit} states serving as computational basis states, such RD computers with operations satisfying a necessary semi-group property could mimic some well known quantum logic gates and carry out teleportation like procedure using entangled states, believed to be a prerogative of the quantum world. Moreover, assuming a nonlinear extension the RD computers could be used for cloning of arbitrary states, which is a famous forbidden operation in standard q...

Kundu, A

2003-01-01

298

Quantum computation in continuous time using dynamic invariants

International Nuclear Information System (INIS)

We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We show that the relaxation of adiabaticity can be achieved by processing information in the eigenlevels of a time dependent observable, namely, the dynamic invariant operator. Moreover, we derive the conditions for which the computation can be implemented by time independent as well as by adiabatically varying Hamiltonians. We illustrate our results by providing the implementation of both Deutsch-Jozsa and Grover algorithms via dynamic invariants. -- Highlights: ? An approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants is introduced. ? Nonadiabatic quantum computation is performed in the eigenlevels of the dynamic invariant operator. ? Condition of equivalence with adiabatic quantum computation is analyzed. ? Implementation of Deutsch-Jozsa and Grover algorithms is provided.

299

Elementary Particles as Gates for Universal Quantum Computation

It is shown that there exists a mapping between the fermions of the Standard Model (SM) represented as braids in the Bilson-Thompson model, and a set of gates which can perform Universal Quantum Computation (UQC). This leads us to conjecture that the "Computational Universe Hypothesis" (CUH) can be given a concrete implementation in a new physical framework where elementary particles and the gauge bosons (which intermediate interactions between fermions) are interpreted as the components of a quantum computational network, with the particles serving as quantum computational gates and the gauge fields as the information carrying entities.

Vaid, Deepak

2013-01-01

300

Digital Repository Infrastructure Vision for European Research (DRIVER)

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}.

Aharonov, Dorit; Vazirani, Umesh

2012-01-01

301

Experimental magic state distillation for fault-tolerant quantum computing

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.

Souza, Alexandre M; Ryan, Colm A; Laflamme, Raymond; 10.1038/ncomms1166

2011-01-01

302

Experimental magic state distillation for fault-tolerant quantum computing.

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. PMID:21266968

Souza, Alexandre M; Zhang, Jingfu; Ryan, Colm A; Laflamme, Raymond

2011-01-25

303

Two-bit gates are universal for quantum computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.

Di Vincenzo, D P

1994-01-01

304

Quantum picturalism for topological cluster-state computing

'Quantum picturalism' is a method for graphically representing processes in quantum mechanics. It is of particular interest for quantum information processes, defining a 'flow' of information through a protocol or algorithm. In this paper we apply the category-theoretic work of Abramsky and Coecke to the topological cluster-state model of quantum computing to show the topological equivalence of defect strands in the cluster state and the graphical flow of the red/green calculus. We concentrate here on the pictorial representation, and use a minimal amount of the machinery of category theory. We give the equivalence between the graphical and topological information flows, and show the applicable rewrite algebra for this computing model. Finally we show how the use of quantum picturalism gives a proof algebra for topological cluster state computing, from which we can derive previously unknown properties of the model. This work not only demonstrates for the first time a concrete realisation of quantum diagrammat...

Horsman, Clare

2011-01-01

305

Continuous-Variable Quantum Computing in Optical Time-Frequency Modes Using Quantum Memories

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.

Humphreys, Peter C.; Kolthammer, W. Steven; Nunn, Joshua; Barbieri, Marco; Datta, Animesh; Walmsley, Ian A.

2014-09-01

306

Continuous-variable quantum computing in optical time-frequency modes using quantum memories.

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. PMID:25302876

Humphreys, Peter C; Kolthammer, W Steven; Nunn, Joshua; Barbieri, Marco; Datta, Animesh; Walmsley, Ian A

2014-09-26

307

Statistical Mechanics of Classical and Quantum Computational Complexity

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.

Laumann, C. R.; Moessner, R.; Scardicchio, A.; Sondhi, S. L.

308

Towards fault-tolerant quantum computing with trapped ions

Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set of quantum logic gates for the implementation of arbitrary quantum operations. As in classical models of computation, quantum error correction techniques enable rectification of small imperfections in gate operations, thus allowing for perfect computation in the presence of noise. For fault-tolerant computation, it is commonly believed that error thresholds ranging between 10^-4 and 10^-2 will be required depending on the noise model and the computational overhead for realizing the quantum gates. Up to now, all experimental implementations have fallen short of these requirements. Here, we report on a Molmer-Sorensen type gate operation entangling ions with a fidelity of 99.3(1)% which together with single-qubit operations forms a universal set of quantum gates. The gate op...

Benhelm, J; Roos, C F; Blatt, R

2008-01-01

309

Mesoporous matrices for quantum computation with improved response through redundance

We present a solid state implementation of quantum computation, which improves previously proposed optically driven schemes. Our proposal is based on vertical arrays of quantum dots embedded in a mesoporous material which can be fabricated with present technology. The redundant encoding typical of the chosen hardware protects the computation against gate errors and the effects of measurement induced noise. The system parameters required for quantum computation applications are calculated for II-VI and III-V materials and found to be within the experimental range. The proposed hardware may help minimize errors due to polydispersity of dot sizes, which is at present one of the main problems in relation to quantum dot-based quantum computation.

Hodgson, T; Leventis, N; D'Amico, I; 10.1063/1.2745438

2009-01-01

310

Spin-based quantum computation using endohedral fullerenes

We describe the design of a spin-based solid-state quantum computer using Group-V C60 endohedral fullerenes. These molecules, comprised of a Carbon-60 Buckmeisterfullerene encapsulating either a Nitrogen or Phosphorous atom, are paramagnetic and possess many unique features that make them ideal components for a spin-based quantum information processor. We describe, in some detail, the physical makeup and operation of a quantum information processing device with endohedrals using both locally addressed and globally addressed architectures. We provide experimental and theoretical data to establish that the resulting designs meets well most of the DiVincenzo criteria for a feasible quantum computer design.

Twamley, Jason

2003-03-01

311

Quantum Computation by Optically Coupled Steady Atoms/Quantum-Dots Inside a Quantum Cavity

We present a model for quantum computation using $n$ steady 3-level atoms kept inside a quantum cavity, or using $n$ quantum-dots (QDs) kept inside a quantum cavity. In this model one external laser is pointed towards all the atoms/QDs, and $n$ pairs of electrodes are addressing the atoms/QDs, so that each atom is addressed by one pair. The energy levels of each atom/QD are controlled by an external Stark field given to the atom/QD by its external pair of electrodes. Transition between two energy levels of an individual atom/ QD are controlled by the voltage on its electrodes, and by the external laser. Interactions between two atoms/ QDs are performed with the additional help of the cavity mode (using on-resonance condition). Laser frequency, cavity frequency, and energy levels are far off-resonance most of the time, and they are brought to the resonance (using the Stark effect) only at the time of operations. Steps for a controlled-NOT gate between any two atoms/QDs have been described for this model. Our model demands some challenging technological efforts, such as manufacturing single-electron QDs inside a cavity. However, it promises big advantages over other existing models which are currently implemented, and might enable a much easier scale-up, to compute with many more qubits.

Pradhan, P.; Wang, K. L.; Roychowdhury, V. P.; Anantram, M. P.; Mor, T.; Saini, Subhash (Technical Monitor)

1999-01-01

312

An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum error-correcting code. The threshold theorem states that it is possible to create a quantum computer to ...

Gottesman, Daniel

2009-01-01

313

Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority

Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any (n-1)/2 (rounded down) cheaters among n players. Previous protocols for these tasks tolerated (n-1)/4 (rounded down) and (n-1)/6 (rounded down) cheaters, respectively. The threshold we achieve is tight - even in the classical case, ``fair'' multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum error-correcting codes, whic...

Ben-Or, Michael; Gottesman, Daniel; Hassidim, Avinatan; Smith, Adam

2008-01-01

314

Architectural design for a topological cluster state quantum computer

International Nuclear Information System (INIS)

The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly non-trivial problem. Scalability in quantum information processing is not just a problem of qubit manufacturing and control but it crucially depends on the ability to adapt advanced techniques in quantum information theory, such as error correction, to the experimental restrictions of assembling qubit arrays into the millions. In this paper, we introduce a feasible architectural design for large scale quantum computation in optical systems. We combine the recent developments in topological cluster state computation with the photonic module, a simple chip-based device that can be used as a fundamental building block for a large-scale computer. The integration of the topological cluster model with this comparatively simple operational element addresses many significant issues in scalable computing and leads to a promising modular architecture with complete integration of active error correction, exhibiting high fault-tolerant thresholds.

315

Fast universal quantum computation with railroad-switch local Hamiltonians

We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea [R. Feynman, Optics News 11, 11 (1985)] and use a railroad-switch-type clock register. The resources required to simulate a quantum circuit with L gates in this model are O(L ) small-dimensional quantum systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L ) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of 3-local adiabatic quantum computation.

Nagaj, Daniel

2010-06-01

316

Architectural design for a topological cluster state quantum computer

Energy Technology Data Exchange (ETDEWEB)

The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly non-trivial problem. Scalability in quantum information processing is not just a problem of qubit manufacturing and control but it crucially depends on the ability to adapt advanced techniques in quantum information theory, such as error correction, to the experimental restrictions of assembling qubit arrays into the millions. In this paper, we introduce a feasible architectural design for large scale quantum computation in optical systems. We combine the recent developments in topological cluster state computation with the photonic module, a simple chip-based device that can be used as a fundamental building block for a large-scale computer. The integration of the topological cluster model with this comparatively simple operational element addresses many significant issues in scalable computing and leads to a promising modular architecture with complete integration of active error correction, exhibiting high fault-tolerant thresholds.

Devitt, Simon J; Munro, William J; Nemoto, Kae [National Institute for Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 (Japan); Fowler, Austin G [Institute for Quantum Computing, University of Waterloo, Waterloo (Canada); Stephens, Ashley M; Greentree, Andrew D; Hollenberg, Lloyd C L [Centre for Quantum Computer Technology, School of Physics, University of Melbourne, Victoria 3010 (Australia)], E-mail: devitt@nii.ac.jp

2009-08-15

317

Is the quantum computer a dream or a nightmare?

International Nuclear Information System (INIS)

Some researchers think that the quantum computer is impracticable in the present state of our knowledge. For them, the promises are elsewhere: lighting the fundamental questions about this physics opposite to intuition. The basic components of the quantum computer is a logic gate. The candidates are ions traps or atoms cavities or photons cavities. The stability of this kind of components during interactions is the key issue due to decoherence. The best work of a quantum computer seems to be the factorization of 15. So the best interest is to progress in our understanding of the mesoscopic systems dissipation. (O.M.)

318

Fully fault tolerant quantum computation with non-deterministic gates

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.

Li, Ying; Stace, Thomas M; Benjamin, Simon C

2010-01-01

319

Encoded Universality in Physical Implementations of a Quantum Computer

We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer using only its naturally available interactions. A key element of this approach is the realization that the fungible nature of quantum information allows for universal manipulations using quantum information encoded in a subspace of the full system Hilbert space, as an alternative to using physical qubits directly. Starting with the interactions intrinsic to the physical system, we show how to determine the possible universality resulting from these interactions over an encoded subspace. We outline a general Lie-algebraic framework which can be used to find the encoding for universality and give several examples relevant to solid-state quantum computing.

Bacon, D J; Lidar, D A; Whaley, K B; Di Vincenzo, D P

2001-01-01

320

Group IV solid state proposals for quantum computation

International Nuclear Information System (INIS)

The discovery of the quantum factorization algorithm more than a decade ago triggered intense interest in exploring possible physical realizations of quantum computers. Among the many solid state proposals, electron and nuclear spins in Si and group IV related materials have long coherence times and the capability of state preparation, gating and read-out using electric, magnetic and optical fields. Proposals involving silicon seek to take advantage of an existing mature technology and the implicit promise of scalability from solid state materials. Nevertheless, building such quantum systems depends in many cases on the development of fabrication techniques with nearly atomic precision. Managing decoherence, initialization and read-out in any quantum computer remains a daunting task. In this review we summarize proposals and recent developments relevant to the possible realization of a quantum computer constructed out of Si (or group IV) materials

321

Preparing topological projected entangled pair states on a quantum computer

Digital Repository Infrastructure Vision for European Research (DRIVER)

Simulating exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states, the G-injective projected entangled pair states (PEPS), on a quantum computer. Important examples include the resonant valence bond states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially wit...

Schwarz, Martin; Temme, Kristan; Verstraete, Frank; Pe?rez Garci?a, David; Cubitt, Toby Stanley

2013-01-01

322

Scalable Quantum Computing based on Spin Qubits in CNT QD

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for quantum processing. We introduce macroscopic quantum memory for the system in a form of injected either magnetic or spin carrying atomic ensemble into the nanotube. CNT provides with a stable atomic trap in finite temperature and with one-dimens...

Stobin?ska, Magdalena; Milburn, Gerard J.; Stobin?ski, Leszek

2009-01-01

323

Quantum Algorithm for Protein Folding and its Computational Complexity

We have studied applications of quantum algorithm for the problems in bioinformatics. The protein folding problem is known as one of the difficult problems which we do not solve in polynomial time of input data. We constructed a quantum algorithm for the protein folding problem using our new quantum binary search algorithm, and discussed its computtational complexity. We prove that the computational complexity is polynomial of the number of molecular in the simulation.

Iriyama, S.; Ohya, M.; Yamato, I.

2013-01-01

324

A Photonic Implementation for the Topological Cluster State Quantum Computer

A new implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for non-linear devices to create a lattice of entangled photons. We give estimates of the minimum efficiencies needed for the detectors, fusion gates and quantum dots, from a numerical simulation.

Herrera-Martí, David A; Jennings, David; Rudolph, Terry

2010-01-01

325

Towards scalable quantum communication and computation: Novel approaches and realizations

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 candidates for naturally error-free quantum computation. We propose a scheme to unambiguously detect the anyonic statistics in spin lattice realizations using ultra-cold atoms in an optical lattice. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit.

Jiang, Liang

326

Diamond for quantum communications, spintronics and quantum computing

International Nuclear Information System (INIS)

Full text: Optically emitting defect centres in diamond display a range of unique quantum properties that offer exciting possibilities for the construction of quantum devices which employ optical read-out In this talk I will review these remarkable properties and explain why diamond is an ideal material for use in the fabrication of (i) single photon sources for quantum communications, (i i) optical fibre-based single spin read out systems and (iii) platforms for the investigation of quantum entanglement in solid state systems. The toolkit of available fabrication strategies will be presented Our most recent results on the fabrication of fibre based single photon sources and all-diamond waveguides and cavities will be reviewed. Copyright (2005) Australian Institute of Physics

327

Quantum computing, phase estimation and applications

In this thesis, attention is paid to small experimental testbed applications with respect to the quantum phase estimation algorithm, the core approach for finding energy eigenvalues. An iterative scheme for quantum phase estimation (IPEA) is derived from the Kitaev phase estimation, a study of robustness of the IPEA utilized as a few-qubit testbed application is performed, and an improved protocol for phase reference alignment is presented. Additionally, a short overview of quantum cryptography is given, with a particular focus on quantum steganography and authentication.

Dob?í?ek, Miroslav

2008-01-01

328

Superradiance as a source of collective decoherence in quantum computers

We argue that superradiance (collective emission) due to radiative coupling of qubit states results in non-local noise, and thus introduces an error source that cannot be corrected using current models of fault-tolerant quantum computation.

Yavuz, D. D.

2014-11-01

329

Universal Quantum Computing (PAT-APPL-10-547 262).

The present invention is directed to systems and methods of providing universal quantum computation that avoid certain external control fields that either are hard or impossible to implement, or are serious sources of decoherence (errors). The systems and...

B. Whaley, J. Vala

2004-01-01

330

Directory of Open Access Journals (Sweden)

Full Text Available The article is devoted to picture the main approaches of increasing the effectiveness of teaching the waves and quantum qualities of the light with application of computer technologies.?????? ?????????? ???????????? ???????? ????????? ?????????? ???????????? ??????? ???????? ????????? ? ????????? ???????????? ?????? ? ????????????? ????’??????? ??????????.

?.?. ?????????

2010-09-01

331

Experimental quantum computing to solve systems of linear equations.

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. PMID:25167475

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

2013-06-01

332

What is a quantum computer, and how do we build one?

The DiVincenzo criteria for implementing a quantum computer have been seminal in focussing both experimental and theoretical research in quantum information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. The question is therefore what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that according to this definition a device is a quantum computer if it obeys the following four criteria: Any quantum computer must (1) have a quantum memory; (2) facilitate a controlled quantum evolution of the quantum memory; (3) include a method for cooling the quantum memory; and (4) provide a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault-tolerantly. We discuss various e...

Perez-Delgado, Carlos A

2009-01-01

333

Secure Entanglement Distillation for Double-Server Blind Quantum Computation

Blind quantum computation is a new secure quantum computing protocol where a client, who does not have enough quantum technologies at her disposal, can delegate her quantum computation to a server, who has a fully fledged quantum computer, in such a way that the server cannot learn anything about the client’s input, output, and program. If the client interacts with only a single server, the client has to have some minimum quantum power, such as the ability of emitting randomly rotated single-qubit states or the ability of measuring states. If the client interacts with two servers who share Bell pairs but cannot communicate with each other, the client can be completely classical. For such a double-server scheme, two servers have to share clean Bell pairs, and therefore the entanglement distillation is necessary in a realistic noisy environment. In this Letter, we show that it is possible to perform entanglement distillation in the double-server scheme without degrading the security of blind quantum computing.

Morimae, Tomoyuki; Fujii, Keisuke

2013-07-01

334

Universal quantum computing with correlated spin-charge states

Digital Repository Infrastructure Vision for European Research (DRIVER)

We propose a universal quantum computing scheme in which the orthogonal qubit states |0i and |1> are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot and gate operations are induced all-electrically by changes in the confinement potential. Within the computational space, these qubits are robust against environmental influences that couple to the system through single-particle channels. Due to the identical spin and charge propertie...

Kyriakidis, Jordan; Burkard, Guido

2007-01-01

335

Simulating Bell violations without quantum computers

We demonstrate that it is possible to simulate Bell violations using probabilistic methods. A quantum state corresponding to optical experiments that violate a Bell inequality is randomly sampled, demonstrating Bell's quantum paradox. This provides an explicit counter-example to Feynman's claim that such classical simulations could not be carried out.

Drummond, P. D.; Opanchuk, B.; Rosales-Zárate, L.; Reid, M. D.

2014-04-01

336

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.

Roland, J; Roland, Jeremie; Cerf, Nicolas J.

2004-01-01

337

Quantum computation from a de Broglie-Bohm perspective

We consider an example of a quantum algorithm from the point of view of the de Broglie-Bohm formulation of quantum mechanics. For concreteness we look at two particular implementations: one using spin-1/2 particles as described by a simple model due to Bell and the other as energy states in an infinite-well potential. We extend the analysis to encompass a complete set of quantum gates. We conclude by discussing the relevance of our investigations for the debate about the origin of the quantum-computational speed-up.

Roser, Philipp

2012-01-01

338

An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (non-universal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) is far weaker than a universal QC, unless supplemented with an additional non-stabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons cannot exhibit non-locality (in the sense of violating a Bell inequality) when only topologically protected stabilizer operations are performed. To produce correlations that cannot be described by an LHV model again requires the use of a non-stabilizer operation. Using geometric techniques, we relate the sets of operations that enable universal QC with those that enable violation of a Bell inequality. Motivated by the fact that non-stabilizer operations are expected to be highly imperfect, our aim is to provide a benchmark for identifying UQC-enabling operations that is both experimentally practical and conceptually simple. We show that any (noisy) single-qubit non-stabilizer operation that, together with perfect stabilizer operations, enables violation of the simplest two-qubit Bell inequality can also be used to enable UQC.

Howard, Mark; Vala, Jiri

2012-02-01

339

Applying Kitaev's algorithm in an ion trap quantum computer

International Nuclear Information System (INIS)

Full text: Kitaev's algorithm is a method of estimating eigenvalues associated with an operator. Shor's factoring algorithm, which enables a quantum computer to crack RSA encryption codes, is a specific example of Kitaev's algorithm. It has been proposed that the algorithm can also be used to generate eigenstates. We extend this proposal for small quantum systems, identifying the conditions under which the algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate a simple example, in which the algorithm effectively generates eigenstates

340

Algorithm-Based Analysis of Collective Decoherence in Quantum Computation

The information in quantum computers is often stored in identical two-level systems (spins or pseudo-spins) that are separated by a distance shorter than the characteristic wavelength of a reservoir which is responsible for decoherence. In such a case, the collective spin-reservoir interaction, rather than an individual spin-reservoir interaction, may determine the decoherence characteristics. We use computational basis states, symmetrized spin states and spin coherent states to study collective decoherence in the implementation of various quantum algorithms. A simple method of implementing quantum algorithms using stable subradiant states and avoiding unstable Dicke's superradiant states and Schrodinger's cat states is proposed.

Utsunomiya, S; Yamamoto, Y; Utsunomiya, Shoko; Master, Cyrus P.; Yamamoto, Yoshihisa

2004-01-01

341

Quantum Computers and Decoherence Exorcising the Demon from the Machine

Decoherence is the main obstacle to the realization of quantum computers. Until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem. Here we present an alternative that is based on a combination of a decoherence-free subspace encoding and the application of strong and fast pulses: ``encoded recoupling and decoupling'' (ERD). This alternative has the advantage of lower encoding overhead (as few as two physical qubits per logical qubit suffice), and direct application to a number of promising proposals for the experimental realization of quantum computers.

Lidar, D A; Lidar, Daniel A.; Wu, Lian-Ao

2003-01-01

342

Approximability of optimization problems through adiabatic quantum computation

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

Cruz-Santos, William

2014-01-01

343

New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy

International Nuclear Information System (INIS)

The power of a quantum computer (QC) relies on the fundamental concept of the superposition in quantum mechanics and thus allowing an inherent large-scale parallelization of computation. In a QC, binary information embodied in a quantum system, such as spin degrees of freedom of a spin-1/2 particle forms the qubits (quantum mechanical bits), over which appropriate logical gates perform the computation. In classical computers, the basic unit of information is the bit, which can take a value of either 0 or 1. Bits are connected together by logic gates to form logic circuits to implement complex logical operations. The expansion of modern computers has been driven by the developments of faster, smaller and cheaper logic gates. As the size of the logic gates become smaller toward the level of atomic dimensions, the performance of such a system is no longer considered classical but is rather governed by quantum mechanics. Quantum computers offer the potentially superior prospect of solving computational problems that are intractable to classical computers such as efficient database searches and cryptography. A variety of algorithms have been developed recently, most notably Shor's algorithm for factorizing long numbers into prime factors in polynomial time and Grover's quantum search algorithm. The algorithms that were of only theoretical interest as recently, until several methods were proposed to build an experimental QC. These methods include, trapped ions, cavity-QED, coupled quantum dots, Josephson junctions, spin resonance transistors, linear optics and nuclear magnetic resonance. Nuclear magnetic resonance (NMR) is uniquely capable of constructing small QCs and several algorithms have been implemented successfully. NMR-QC differs from other implementations in one important way that it is not a single QC, but a statistical ensemble of them. Thus, quantum computing based on NMR is considered as ensemble quantum computing. In NMR quantum computing, the spins with non-zero nuclear moments (spin 1/2 nuclei such as 1H or 13C) in an organic molecule dissolved in a solvent constitute the required qubits. The logic gates and algorithms correspond to set of instructions containing radio frequency (r.f) pulses and delays that manipulate the qubits and the final spectrum reflects the outcome of the algorithm. Three years ago, when we initiated proposal on NMR-QC, the foremost of the aim is to develop quantum computing as part of LLNL research programs and hence cultivate an interdisciplinary working group in the area of quantum computing. Our success in the proposal is in part responsible for the formation of the laboratory-wide exploratory group on ''quantum computing and information''. The PI's play an integral role in promoting the work performed using the LDRD funded project and hence acquire the attention within the lab as well outside. In specific goals of the project were to (a) develop experimental and sample based methods to improve the performance of NMR-QC, (b) define and estimate actual time cost or efficiency of a QCs, and (c) construct a comprehensive simulator of QC based on the principles of ensemble quantum computing. We were able to accomplish these goals and in particular we have reached some significant milestones in defining the QC efficiency and development of the QC-simulator. These developments have resulted to three publications

344

Exponential rise of dynamical complexity in quantum computing through projections

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.

Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya

2014-10-01

345

Exponential rise of dynamical complexity in quantum computing through projections.

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. PMID:25300692

Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya

2014-01-01

346

Continuous-Variable Quantum Computing in Optical Time-Frequency Modes using Quantum Memories

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 2D 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 is a linear function of only the number of different freq...

Humphreys, Peter C.; Kolthammer, W. Steven; Nunn, Joshua; Barbieri, Marco; Datta, Animesh; Walmsley, Ian A.

2014-01-01

347

Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity

Digital Repository Infrastructure Vision for European Research (DRIVER)

We investigate the possibility to achieve 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-qu...

Wei, Hai-rui; Deng, Fu-guo

2013-01-01

348

Exact Master Equation and Non-Markovian Decoherence for Quantum Dot Quantum Computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman-Vernon influence functional approach. The exact master equation is valid for general nanostructure systems coupled to multi-reservoirs with arbitrary spectral densities, temperatures and biases. We take the double quantum dot charge qubit system as a specific example, and discuss ...

Tu, Matisse W. Y.; Lee, Ming-tsung; Zhang, Wei-min

2009-01-01

349

Simultaneous intraportation of many quantum states within the quantum computing network

Digital Repository Infrastructure Vision for European Research (DRIVER)

A scheme is proposed for simultaneous intraportation of many unknown quantum states within a quantum computing network. It is shown that our scheme, much different from the teleportation in the strict sense, can be very similar to the original teleportation proposal[Phys.Rev.Lett.{\\bf 70} (1993)1895)] and the efficiency of the scheme for quantum state transmission is very high. The possible applications of our scheme are also discussed.

Feng, Mang

2001-01-01

350

Combined Error Correction Techniques for Quantum Computing Architectures

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...

Byrd, M S; Byrd, Mark S.; Lidar, Daniel A.

2003-01-01

351

Quantum triangulations. Moduli spaces, strings, and quantum computing

International Nuclear Information System (INIS)

Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications. (orig.)

352

Computations in Finite Groups and Quantum Physics

Digital Repository Infrastructure Vision for European Research (DRIVER)

Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing "unobservable" elements in their descriptions. Since our aim is physics where the choice between finite and infinite descriptions can not have any empirical consequences, we consider the problem in the finite background. Besides, there are many i...

Kornyak, Vladimir V.

2011-01-01

353

LDRD final report on quantum computing using interacting semiconductor quantum wires.

Energy Technology Data Exchange (ETDEWEB)

For several years now quantum computing has been viewed as a new paradigm for certain computing applications. Of particular importance to this burgeoning field is the development of an algorithm for factoring large numbers which obviously has deep implications for cryptography and national security. Implementation of these theoretical ideas faces extraordinary challenges in preparing and manipulating quantum states. The quantum transport group at Sandia has demonstrated world-leading, unique double quantum wires devices where we have unprecedented control over the coupling strength, number of 1 D channels, overlap and interaction strength in this nanoelectronic system. In this project, we study 1D-1D tunneling with the ultimate aim of preparing and detecting quantum states of the coupled wires. In a region of strong tunneling, electrons can coherently oscillate from one wire to the other. By controlling the velocity of the electrons, length of the coupling region and tunneling strength we will attempt to observe tunneling oscillations. This first step is critical for further development double quantum wires into the basic building block for a quantum computer, and indeed for other coupled nanoelectronic devices that will rely on coherent transport. If successful, this project will have important implications for nanoelectronics, quantum computing and information technology.

Lyo, Sungkwun Kenneth; Dunn, Roberto G.; Lilly, Michael Patrick; Tibbetts, Denise R. (.; )); Stephenson, Larry L.; Seamons, John Andrew; Reno, John Louis; Bielejec, Edward Salvador; Simmons, Jerry Alvon

2006-01-01

354

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Comment on the paper "Quantum waveguide array generator for performing Fourier transforms: Alternate route to quantum computing" by R. Akis and D.K. Ferry, Appl. Phys. Lett. 79, 2823 (2001). The authors reply in Appl. Phys. Lett. 80, 2420 (2002).

Lidar, Daniel A.

2003-01-01

355

Quantum Monte Carlo Endstation for Petascale Computing

Energy Technology Data Exchange (ETDEWEB)

The major achievements enabled by QMC Endstation grant include * Performance improvement on clusters of x86 multi-core systems, especially on Cray XT systems * New and improved methods for the wavefunction optimizations * New forms of trial wavefunctions * Implementation of the full application on NVIDIA GPUs using CUDA The scaling studies of QMCPACK on large-scale systems show excellent parallel efficiency up to 216K cores on Jaguarpf (Cray XT5). The GPU implementation shows speedups of 10-15x over the CPU implementation on older generation of x86. We have implemented hybrid OpenMP/MPI scheme in QMC to take advantage of multi-core shared memory processors of petascale systems. Our hybrid scheme has several advantages over the standard MPI-only scheme. * Memory optimized: large read-only data to store one-body orbitals and other shared properties to represent the trial wave function and many-body Hamiltonian can be shared among threads, which reduces the memory footprint of a large-scale problem. * Cache optimized: the data associated with an active Walker are in cache during the compute-intensive drift-diffusion process and the operations on an Walker are optimized for cache reuse. Thread-local objects are used to ensure the data affinity to a thread. * Load balanced: Walkers in an ensemble are evenly distributed among threads and MPI tasks. The two-level parallelism reduces the population imbalance among MPI tasks and reduces the number of point-to-point communications of large messages (serialized objects) for the Walker exchange. * Communication optimized: the communication overhead, especially for the collective operations necessary to determine ET and measure the properties of an ensemble, is significantly lowered by using less MPI tasks. The multiple forms of parallelism afforded by QMC algorithms make them ideal candidates for acceleration in the many-core paradigm. We presented the results of our effort to port the QMCPACK simulation code to the NVIDIA CUDA GPU platform. We restructured the CPU algorithms to express additional parallelism, minimize GPU-CPU communication, and efficiently utilize the GPU memory hierarchy. Using mixed precision on GT200 GPUs and MPI for intercommunication and load balancing, we observe typical full-application speedups of approximately 10x to 15x relative to quad-core Xeon CPUs alone, while reproducing the double-precision CPU results within statistical error. We developed an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and used it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We computed the static contribution to the free energy with the QMC method and obtained the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We computed the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy. We compared experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron momentum density, we derived its discontinuity at the Fermi wavevector finding an accurate measure of the renormalization factor that we compared with quantum-Monte-Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas. Our calculated results are in good agreement with the experiment. We have been studying the heat of formation for various Kubas complexes of molecular hydrogen on Ti(1,2)ethylene-nH2 using Diffusion Monte Carlo. This work has been started and is o

David Ceperley

2011-03-02

356

Possible schemes of calculation modeling in a quantum computer

Directory of Open Access Journals (Sweden)

Full Text Available In the present work a possibility of computation modeling, which should be realized in a real quantum computer, is discussed. In this connection two models of a device, which work is determined by the structure and dynamics of real molecular systems are reported.

Vladimir Voronov

2010-08-01

357

From transistor to trapped-ion computers for quantum chemistry.

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. PMID:24395054

Yung, M-H; Casanova, J; Mezzacapo, A; McClean, J; Lamata, L; Aspuru-Guzik, A; Solano, E

2014-01-01

358

Holonomic Quantum Computation with Electron Spins in Quantum Dots

Digital Repository Infrastructure Vision for European Research (DRIVER)

With the help of the spin-orbit interaction, we propose a scheme to perform holonomic single qubit gates on the electron spin confined to a quantum dot. The manipulation is done in the absence (or presence) of an applied magnetic field. By adiabatic changing the position of the confinement potential, one can rotate the spin state of the electron around the Bloch sphere in semiconductor heterostructures. The dynamics of the system is equivalent to employing an effective non-A...

Golovach, Vitaly N.; Borhani, Massoud; Loss, Daniel

2009-01-01

359

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.

D'Ariano, Giacomo Mauro

2010-05-01

360

Towards a fullerene-based quantum computer

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.

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

361

Quantum theory of decoherence in solid-state spin quantum computing architectures

Decoherence is the adversary of any proposed quantum computer. In order to overcome it, we must understand it. Nuclear induced spectral diffusion, a type of electron spin decoherence caused by interaction with a nuclear spin bath, is a predominant source of information loss for solid-state spin quantum computing architectures. All previous theories for this 50-year-old problem have used phenomenological, semi-classical models. This talk presents our cluster expansion method which provides the first fully microscopic and quantum mechanical solution to this problem. With our method it becomes possible to ascertain the effectiveness of pulse sequences designed to enhance spin coherence.

Witzel, Wayne; Das Sarma, Sankar

2006-03-01

362

One of the basics tasks in computer systems is the control of access of resources. Basically, there is a finite amount of resources that can be, for example, the CPU, memory or I/O ports, and several processes requiring those resources. If there is not enough resource in order to attend the demand, some kind of control access has to be employed. In this work, recognizing the resource sharing problem as a competition, we employ a simplified multiplayer quantum game as an access controller. The proposed quantum game can be employed in the architecture of quantum computers.

de Sousa, Paulo Benicio Melo

2008-01-01

363

Experimental demonstration of measurement-based quantum computation in correlation space

The paradigm of measurement-based quantum computation opens new experimental avenues to realize a quantum computer and deepens the understanding of quantum physics. For years, the entanglement properties of cluster states have been considered critical for universal measurement- based quantum computation. Surprisingly, a novel framework namely quantum computation in correlation space has opened new routes to construct quantum states possessing entanglement properties different from cluster states while still retaining the universality for measurement-based quantum computing. The scheme not only offers more flexibility to prepare universal resources for quantum computation, but also provides a different perspective to study the fundamental problem regarding what are the essential features responsible for the speedup of quantum computers over classical devices. Here we report an experimental realization of every building block of the model of measurement-based quantum computation in correlation space. In the exp...

Gao, Wei-Bo; Cai, Jian-Ming; Lu, He; Xu, Ping; Yang, Tao; Chen, Yu-Ao; Chen, Zeng-Bing; Pan, Jian-Wei

2010-01-01

364

Quantum information and computation for chemistry

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

Kais, Sabre; Rice, Stuart A

2014-01-01

365

Could one make a diamond-based quantum computer?

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. PMID:21832328

Stoneham, A Marshall; Harker, A H; Morley, Gavin W

2009-09-01

366

Weak nonlinearities: a new route to optical quantum computation

International Nuclear Information System (INIS)

Quantum information processing (QIP) offers the promise of being able to do things that we cannot do with conventional technology. Here we present a new route for distributed optical QIP, based on generalized quantum non-demolition measurements, providing a unified approach for quantum communication and computing. Interactions between photons are generated using weak nonlinearities and intense laser fields-the use of such fields provides for robust distribution of quantum information. Our approach only requires a practical set of resources, and it uses these very efficiently. Thus it promises to be extremely useful for the first quantum technologies, based on scarce resources. Furthermore, in the longer term this approach provides both options and scalability for efficient many-qubit QIP

367

Making and manipulating Majorana fermions for topological quantum computation

International Nuclear Information System (INIS)

Known theoretically for decades, Majorana fermions have never been observed as fundamental particles. But there is growing excitement among condensed matter physicists that Majorana fermions could be observed as quasiparticles in the solid state. This excitement is fueled by their remarkable properties: They are their own antiparticle and obey an exotic (and yet unobserved) form of quantum statistics called non-Abelian statistics. These properties make Majorana fermions the simplest candidate for realizing topological quantum information processing which could go a long way towards alleviating the problem of decoherence in conventional quantum computation. Among the systems predicted to support Majorana fermions are exotic fractional quantum Hall states as well as hybrid structures of topological insulators, semimetals, or semiconductors with conventional superconductors. Realizations based on semiconductor quantum wires in proximity to conventional superconductors are perhaps particularly promising since they allow for relatively detailed scenarios of how to manipulate the Majorana fermions. In this talk, I discuss this proposal to realize Majorana fermions.

368

We present a model for quantum computation using n steady 3-level atoms or3-level quantum dots, kept inside a quantum electro-dynamics (QED) cavity. Ourmodel allows one-qubit operations and the two-qubit controlled-NOT gate asrequired for universal quantum computation. The n quantum bits are described bytwo energy levels of each atom/dot. An external laser and n separate pairs ofelectrodes are used to address a single atom/dot independent of the others, viaStark effect. The third level of each system and an additional common-modequbit (a cavity photon) are used for realizing the controlled-NOT operationbetween any pair of qubits. Laser frequency, cavity frequency, and energylevels are far off-resonance, and they are brought to resonance by modifyingthe energy-levels of a 3-level system using the Stark effect, only at the timeof operation.

Pradhan, P; Wang Ke Lin; Pradhan, Prabhakar; Wang, Kang L.

2000-01-01

369

Method of quantum computation with "hot" trapped ions

We present a novel method of performing quantum logic gates in trapped ion quantum computers which does not require the ions to be cooled down to their vibrational center of mass (CM) mode ground state. Our scheme employs adiabatic passages and the conditional phase shift first investigated by D'Helon and Milburn (C.~D'Helon and G.J.~Milburn, Phys. Rev. A {\\bf 54}, 5141 (1996)).

Schneider, S; Milburn, G J; Schneider, Sara; James, Daniel F.V.; Milburn, Gerard J.

1998-01-01

370

A quantum computer based on electrons floating on liquid helium

Digital Repository Infrastructure Vision for European Research (DRIVER)

Electrons on a helium surface form a quasi two-dimensional system which displays the highest mobility reached in condensed matter physics. We propose to use this system as a set of interacting quantum bits. We will briefly describe the system and discuss how the qubits can be addressed and manipulated, including interqubit excitation transfer. The working frequency of the proposed quantum computer is ~1GHz. The relaxation rate can be at least 5 orders of magnitude smaller, f...

Dykman, M. I.; Platzman, P. M.

2001-01-01

371

Multilevel distillation of magic states for quantum computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

We develop a procedure for distilling magic states used in universal quantum computing that requires substantially fewer initial resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes that possess a transversal Hadamard operation, enabling each of these codes to distill the eigenstate of the Hadamard operator. A crucial result of this design is that low-fidelity magic states can be consumed to purify other high-fidelity magi...

Jones, Cody

2012-01-01

372

Experimental characterization of universal one-way quantum computing

Digital Repository Infrastructure Vision for European Research (DRIVER)

We report the characterization of a universal set of logic gates for one-way quantum computing using a four-photon `star' cluster state generated by fusing photons from two independent photonic crystal fibre sources. We obtain a fidelity for the cluster state of 0.66 +/- 0.01 with respect to the ideal case. We perform quantum process tomography to completely characterize a controlled-NOT, Hadamard and T gate all on the same compact entangled resource. Together, these operati...

Bell, B. A.; Tame, M. S.; Clark, A. S.; Nock, R. W.; Wadsworth, W. J.; Rarity, J. G.

2013-01-01

373

Many Worlds, the Cluster-state Quantum Computer, and the Problem of the Preferred Basis

I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.

Cuffaro, Michael

2011-01-01

374

A computable framework for Loop Quantum Gravity

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The methods of loop quantum gravity applied to this model lead to a physical Hilbert space and Hamiltonian. This provides a framework for physical calculations in the theory.

Husain, Viqar; Pawlowski, Tomasz

2013-01-01

375

Oxford ion-trap quantum computing project.

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. PMID:12869316

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

376

Individual addressing in quantum computation through spatial refocusing

Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains a significant source of error for current experimental implementations of multiqubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk error for any type of quantum gate. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show that the crosstalk-induced infidelity of quantum gates can be reduced by several orders of magnitude with a moderate cost of a few correction laser beams under typical experimental conditions.

Shen, C.; Gong, Z.-X.; Duan, L.-M.

2013-11-01

377

Computer studies of multiple-quantum spin dynamics

International Nuclear Information System (INIS)

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

378

Scalable Quantum Computing based on Spin Qubits in CNT QD

We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for quantum processing. We introduce macroscopic quantum memory for the system in a form of injected either magnetic or spin carrying atomic ensemble into the nanotube. CNT provides with a stable atomic trap in finite temperature and with one-dimensional nuclear spin lattice in an external magnetic field. The electron is coupled to the atomic ensemble through either magnetic or hyperfine interaction. Easy electron and nuclear spin read-out procedure for this system is possible.

Stobi?ska, Magdalena; Stobi?ski, Leszek

2009-01-01

379

On the Physical Explanation for Quantum Computational Speedup

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...

Cuffaro, Michael E

2013-01-01

380

Computer science approach to quantum control

International Nuclear Information System (INIS)

es 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 definitions of complexity in computer science must be based upon a notion of elementary computation steps that correspond to not too complex real physical processes. This book tries to shed light on both aspects of this unification. (orig.)

381

Quantum picturalism for topological cluster-state computing

Energy Technology Data Exchange (ETDEWEB)

Topological quantum computing (QC) is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of computing is a leading candidate for large-scale QC. However, there has been a lack of sufficiently powerful high-level languages to describe computing in this form without resorting to single-qubit operations, which quickly become prohibitively complex as the system size increases. In this paper, we apply the category-theoretic work of Abramsky and Coecke to the topological cluster-state model of QC to give a high-level graphical language that enables direct translation between quantum processes and physical patterns of measurement in a computer-a 'compiler language'. We give the equivalence between the graphical and topological information flows, and show the applicable rewrite algebra for this computing model. We show that this gives us a native graphical language for the design and analysis of topological quantum algorithms, and finish by discussing the possibilities for automating this process on a large scale.

Horsman, Clare, E-mail: clare@sfc.wide.ad.jp [Oxford University Computing Laboratory, Parks Road, Oxford OX1 3QD, UK and Keio University Shonan Fujisawa Campus, Fujisawa, Kanagawa 252-0882 (Japan)

2011-09-15

382

Quadratic Hamiltonian for quantum computation with continuous variables

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. These Hamiltonians (i) are quadratic, and therefore two-body; (ii) are of short range, involving only up to next-to-nearest-neighbour interactions; and (iii) possess a constant gap proportional to the squared inverse of a squeezing parameter $s$. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation at criticality ($s\\rightarrow\\infty$). These Hamiltonians constitute the basic ingredient required for the adiabatic preparation of graph states. This is particularly important in scenarios where large-scale graph states are necessary, as might likely be the case in fault-tolerant schemes for quantum computing. We characterize the correlations in these systems at thermal equilibrium: In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.

Aolita, Leandro; Ferraro, Alessandro; Acín, Antonio

2010-01-01

383

Ground-state geometric quantum computing in superconducting systems

We present a theoretical proposal for the implementation of geometric quantum computing based on a Hamiltonian which has a doubly degenerate ground state. Thus the system which is steered adiabatically, remains in the ground-state. The proposed physical implementation relies on a superconducting circuit composed of three SQUIDs and two superconducting islands with the charge states encoding the logical states. We obtain a universal set of single-qubit gates and implement a nontrivial two-qubit gate exploiting the mutual inductance between two neighboring circuits, allowing us to realize a fully geometric ground-state quantum computing. The introduced paradigm for the implementation of geometric quantum computing is expected to be robust against environmental effects.

Solinas, P.; Pirkkalainen, J.-M.; Möttönen, M.

2010-11-01

384

Scalable quantum computation in systems with Bose-Hubbard dynamics

Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In [1] we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.

Pupillo, G; Brennen, G; Williams, C J; Clark, C W; Pupillo, Guido; Rey, Ana Maria; Brennen, Gavin; Williams, Carl J.; Clark, Charles W.

2004-01-01

385

Towards molecular energy calculations on a quantum computer

The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. In principle, the total energy of a molecule, as well as most other properties, can be calculated by solving the Schr\\"odinger equation. However, the computational resources required to obtain exact solutions on a conventional computer generally increase exponentially with the number of atoms involved. Recently, an algorithm has been proposed that enables a quantum computer to calculate molecular energies in a time that increases only polynomially in the molecular size. Here we present a quantum optical implementation for the smallest problem: obtaining the energies of the hydrogen molecule, H2, in a minimal basis. We perform a key algorithmic step - the iterative phase estimation algorithm - in full, achieving a high level of precision and robustness to error. We perform other algorithmic steps with assistance from a classic...

Lanyon, Benjamin P; Gillet, Geoff G; Goggin, Michael E; Almeida, Marcelo P; Kassal, Ivan; Biamonte, Jacob D; Mohseni, Masoud; Powell, Ben J; Barbieri, Marco; Aspuru-Guzik, Alán; White, Andrew G

2009-01-01

386

Cluster-state quantum computation: the role of entanglement

Energy Technology Data Exchange (ETDEWEB)

Cluster-state quantum computation is computationally equivalent to the traditional circuit model, but the pictures of computational processes outlined by the two are radically different. Here are investigated some of the consequences of this situation for the explanation of the quantum speed-up, whit particular regard to the role played by entanglement. At first sight, the evolution of a cluster-state computer seems to be disentangling (at each step one qubit is measured and discarded), but in a fully-unitary dynamical account it appears to be entangling (at each step a correlation is established between one qubit and its respective recorder). It is thus suggested that the different uses made of the features of quantum systems by the two frameworks, do not rule out the thesis that the speed-up is achieved by means of an entangling transformation. However, in this last case entanglement is created step by step, and thus the main difference between the two frameworks seems to remain the absence of ''quantum parallelism''. The only entangling-generating unitary transformations acting at the same time on all the qubits are the controlled-phase operation involved in the preparation of the cluster. Thus, the explanation of the quantum speed-up should be looked for just in these type of transformations.

Annovi, Filippo [Department of Philosophy, University of Bologna (Italy)

2013-07-01

387

Cluster-state quantum computation: the role of entanglement

International Nuclear Information System (INIS)

Cluster-state quantum computation is computationally equivalent to the traditional circuit model, but the pictures of computational processes outlined by the two are radically different. Here are investigated some of the consequences of this situation for the explanation of the quantum speed-up, whit particular regard to the role played by entanglement. At first sight, the evolution of a cluster-state computer seems to be disentangling (at each step one qubit is measured and discarded), but in a fully-unitary dynamical account it appears to be entangling (at each step a correlation is established between one qubit and its respective recorder). It is thus suggested that the different uses made of the features of quantum systems by the two frameworks, do not rule out the thesis that the speed-up is achieved by means of an entangling transformation. However, in this last case entanglement is created step by step, and thus the main difference between the two frameworks seems to remain the absence of ''quantum parallelism''. The only entangling-generating unitary transformations acting at the same time on all the qubits are the controlled-phase operation involved in the preparation of the cluster. Thus, the explanation of the quantum speed-up should be looked for just in these type of transformations.

388

Cellular Structures for Computation in the Quantum Regime

We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking avoids the time-scale problems associated with ground-state relaxation schemes. For quantum computing, the architecture constitutes a novel paradigm whereby the algorithm is embedded in spatial, as opposed to temporal, structure. The architecture can be exploited to produce highly efficient algorithms: for example, a list of length N can be searched in time of order cube root N.

Benjamin, S C

1999-01-01

389

Computational Physics Simulation of Classical and Quantum Systems

This book encapsulates the coverage for a two-semester course in computational physics. The first part introduces the basic numerical methods while omitting mathematical proofs but demonstrating the algorithms by way of numerous computer experiments. The second part specializes in simulation of classical and quantum systems with instructive examples spanning many fields in physics, from a classical rotor to a quantum bit. All program examples are realized as Java applets ready to run in your browser and do not require any programming skills.

Scherer, Philipp O. J

2010-01-01

390

Reversible CAM Processor Modeled After Quantum Computer Behavior

Proposed below is a reversible digital computer modeled after the natural behavior of a quantum system. Using approaches usually reserved for idealized quantum computers, the Reversible CAM, or State Vector Parallel (RSVP) processor can easily find keywords in an unstructured database (that is, it can solve a needle in a haystack problem). The RSVP processor efficiently solves a SAT (Satisfiability of Boolean Formulae) problem; also it can aid in the solution of a GP (Global Properties of Truth Table) problem. The power delay product of the RSVP processor is exponentially lower than that of a standard CAM programmed to perform similar operations.

Burger, J R

2005-01-01

391

Computational physics. Simulation of classical and quantum systems

Energy Technology Data Exchange (ETDEWEB)

This book encapsulates the coverage for a two-semester course in computational physics. The first part introduces the basic numerical methods while omitting mathematical proofs but demonstrating the algorithms by way of numerous computer experiments. The second part specializes in simulation of classical and quantum systems with instructive examples spanning many fields in physics, from a classical rotor to a quantum bit. All program examples are realized as Java applets ready to run in your browser and do not require any programming skills. (orig.)

Scherer, Philipp O.J. [TU Muenchen (Germany). Physikdepartment T38

2010-07-01

392

Magnetic resonance force microscopy and a solid state quantum computer.

Energy Technology Data Exchange (ETDEWEB)

A Quantum Computer (QC) is a device that utilizes the principles of Quantum Mechanics to perform computations. Such a machine would be capable of accomplishing tasks not achievable by means of any conventional digital computer, for instance factoring large numbers. Currently it appears that the QC architecture based on an array of spin quantum bits (qubits) embedded in a solid-state matrix is one of the most promising approaches to fabrication of a scalable QC. However, the fabrication and operation of a Solid State Quantum Computer (SSQC) presents very formidable challenges; primary amongst these are: (1) the characterization and control of the fabrication process of the device during its construction and (2) the readout of the computational result. Magnetic Resonance Force Microscopy (MRFM)--a novel scanning probe technique based on mechanical detection of magnetic resonance-provides an attractive means of addressing these requirements. The sensitivity of the MRFM significantly exceeds that of conventional magnetic resonance measurement methods, and it has the potential for single electron spin detection. Moreover, the MRFM is capable of true 3D subsurface imaging. These features will make MRFM an invaluable tool for the implementation of a spin-based QC. Here we present the general principles of MRFM operation, the current status of its development and indicate future directions for its improvement.

Pelekhov, D. V. (Denis V.); Martin, I. (Ivar); Suter, A. (Andreas); Reagor, D. W. (David W.); Hammel, P. C. (P. Chris)

2001-01-01

393

Principles of quantum computation and information volume II

International Nuclear Information System (INIS)

ions, but how you approach them will profoundly determine the character of your book. The authors of 'Principles of Quantum Computation and Information (Volume II: Basic Tools and Special Topics)' have chosen to focus on the construction of quantum computers, but restrict themselves mainly to general techniques. Only in the last chapter do they explicitly address the issues that arise in the different implementations. The book is the second volume in a series, and consists of four chapters (labelled 5 to 8) called 'Quantum Information Theory', 'Decoherence', 'Quantum Error Correction', and 'First Experimental Implementations'. The first volume covers the basics of classical computation, quantum mechanics, quantum computation, and quantum communication. Chapter five starts with the density matrix formalism, and proceeds with the development of the Kraus representation, POVMs, von Neuman entropy, quantum data compression, the Holevo bound, the partial transpose criterion, and it ends with a very nice section on the various entropies that play a role in modern physics. This includes not only the thermodynamical and statistical entropy, but also the dynamical Kolmogorov-Sinai entropy, which is used in quantum chaos in chapter 6. On the whole, I think that this is a really clear and well-presented chapter. A minor drawback is that the concept of CP maps is not explained as well as it could have been, for example by relating it to the partial transpose criterion. Chapter six continues with the high standard set in chapter five, and presents a very thorough exposition of decoherence in general. It introduces the different decoherence channels, and gives truly excellent explanations of the master equation (tied in with the Kraus representation), quantum jumps, and the quantum trajectory formalism. It also has an elegant explanation for the sensitivity of Schroedinger cats to decoherence. The chapter ends with two sections on quantum chaos. Since the authors are experts in this fascinating area, this is a welcome addition to the canon of topics typically covered in quantum information. Unfortunately, the section is quite hard to follow, and as a result it is a bit of a missed opportunity. There is a section on chaos in the first volume of this series, and this may provide the required background. Chapter seven on quantum error correction is disappointing, and I have the feeling that the authors went through the motions without a real passion for the subject matter. The chapter describes various error correction codes, including Hamming codes and CSS codes, but it is virtually silent on fault tolerance; it does not give examples of universal sets of fault tolerant gates, and it does not mention the Solovay-Kitaev theorem. Also, it does not present the stabilizer formalism. All of these are serious omissions in a textbook on quantum information theory. Chapter eight gives a rough sketch of the early simulations and implementations of quantum gates. The readers of this journal will have no trouble following this chapter, but the undergraduate in computer science or mathematics will be completely lost. The chapter covers NMR, cavity QED, ion traps, solid state qubits, and optical implementations of quantum communication. I would have liked to see a more bold choice for the topics covered in the last chapter. For example, whereas liquid-state NMR was an important step in the development of quantum technologies, and many current techniques were invented for it, it does no longer play a role in the design of quantum computers. It would have been better to introduce these techniques in a section on condensed matter systems. Also, as a snapshot of our current state of knowledge in quantum information, I really miss extensive sections on the one-way model of quantum computing and topological quantum computing. In conclusion, the second volume of 'Principles of Quantum Computation and Information' is a partial success. The first two chapters are very good, and I would happily pay Pounds 22 for these two chapters alone. However, for a text o

394

Quantum features of consciousness, computers and brain

Many people believe that mysterious phenomenon of consciousness may be connected with quantum features of our world. The present author proposed so-called Extended Everett's Concept (EEC) that allowed to explain consciousness and super-consciousness (intuitive knowledge). Brain, according to EEC, is an interface between consciousness and super-consciousness on the one part and body on the other part. Relations between all these components of the human cognitive system are analyzed in the framework of EEC. It is concluded that technical devices improving usage of super-consciousness (intuition) may exist.

Mensky, Michael B

2009-01-01

395

Interplay between computable measures of entanglement and other quantum correlations

Composite quantum systems can be in generic states characterized not only by entanglement, but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D_G. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship $D_G \\geq N^2$ holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, that we conjecture to be universal, between two relevant and experimentally friendly...

Girolami, Davide; 10.1103/PhysRevA.84.052110

2011-01-01

396

Graphene quantum dots for valley-based quantum computing: A feasibility study

Digital Repository Infrastructure Vision for European Research (DRIVER)

At the center of quantum computing1 realization is the physical implementation of qubits - two-state quantum information units. The rise of graphene2 has opened a new door to the implementation. Because graphene electrons simulate two-dimensional relativistic particles with two degenerate and independent energy valleys,3 a novel degree of freedom (d.o.f.), namely, the valley state of an electron, emerges as a new information carrier.4 Here, we expand the Loss-DiVincenzo quan...

Wu, G. Y.; Lue, N. -y; Chang, L.

2011-01-01

397

From Fermat's last theorem to the quantum computer

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...

Vlasov, A Yu

2003-01-01

398

Scalable register initialization for quantum computing in an optical lattice

The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation.

Brennen, G K; Rey, A M; Clark, C W; Williams, C J; Brennen, Gavin K.; Pupillo, Guido; Rey, Ana Maria; Clark, Charles W.; Williams, Carl J.

2003-01-01

399

Noise-Resistant Distributed Quantum Computation in Trapped Ion Chain

We consider experimentally feasible chains of trapped ions with pseudo-spin half, and find models that can potentially be used to implement fault tolerant quantum computation. We consider protocols for implementing a universal set of quantum logic gates in the system, by adiabatic passage of a few low-lying energy levels of the whole system. We show that the fidelity of the computation remains virtually unchanged, when introducing noise to the system, if the noise is not too strong. The noise resistance of the system is achieved by encoding the qubits as distributed over the whole system, and is similar in spirit to that of classical neural networks. We call, therefore, our system as a quantum neural network.

Braungardt, S; Lewenstein, M; Sen, U; Braungardt, Sibylle; De, Aditi Sen; Lewenstein, Maciej; Sen, Ujjwal

2006-01-01

400

Indications for quantum computation requirements from comparative brain analysis

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.

Bernroider, Gustav; Baer, Wolfgang

2010-04-01

401

Quantum dots for lasers, amplifiers and computing

International Nuclear Information System (INIS)

For InAs-GaAs based quantum dot lasers emitting at 1300 nm, digital modulation showing an open eye pattern up to 12 Gb s-1 at room temperature is demonstrated, at 10 Gb s-1 the bit error rate is below 10-12 at -2 dB m receiver power. Cut-off frequencies up to 20 GHz are realised for lasers emitting at 1.1 ?m. Passively mode-locked QD lasers generate optical pulses with repetition frequencies between 5 and 50 GHz, with a minimum Fourier limited pulse length of 3 ps. The uncorrelated jitter is below 1 ps. We use here deeply etched narrow ridge waveguide structures which show excellent performance similar to shallow mesa structures, but a circular far field at a ridge width of 1 ?m, improving coupling efficiency into fibres. No beam filamentation of the fundamental mode, low a-factors and strongly reduced sensitivity to optical feedback are observed. QD lasers are thus superior to QW lasers for any system or network. Quantum dot semiconductor optical amplifier (QD SOAs) demonstrate gain recovery times of 120-140 fs, 4-7 times faster than bulk/QW SOAs, and a net gain larger than 0.4 dB/(mm*QD-layer) providing us with novel types of booster amplifiers and Mach-Zehnder interferometers. These breakthroughs became possible due to systematic development of self-organized growth technologies

402

Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer

International Nuclear Information System (INIS)

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 cluster-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

403

Graphical Reasoning in Compact Closed Categories for Quantum Computation

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.

Dixon, Lucas

2009-01-01

404

A Prospect for Future Generation of Quantum Dots in Computers

Directory of Open Access Journals (Sweden)

Full Text Available In this study, first we described the different proposed design of QCAs and their functions. Then we described cell to cell interaction in the presence of external clocking voltage and finally we designed a 4-bit computer using a 4-bit processor which can be used as an 8-bit computer. This design study is based on this specification of 4-bit accumulator so that 8-bit data can be parallel processed in even and odd clock cycles. Our aim is to provide some evidences that quantum dot computers have the potential of increasing their word length and data capacity.

Mirmansour Ziabari

2008-01-01

405

Concatenating dynamical decoupling with decoherence-free subspaces for quantum computation

International Nuclear Information System (INIS)

A scheme to implement a quantum computer subjected to decoherence and governed by an untunable qubit-qubit interaction is presented. By concatenating dynamical decoupling through bang-bang (BB) pulse with decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced decoherence that results in quantum information dissipating into the environment. For the inherent qubit-qubit interaction that is untunable in the quantum system, BB control plus DFSs encoding will eliminate its undesired effect which spoils quantum information in qubits. We show how this quantum system can be used to implement universal quantum computation

406

Concatenating bang-bang control with decoherence-free subspaces for quantum computation

A scheme to implement a quantum computer subjected to decoherence and governed by un-tunable qubit-qubit interaction is presented. By concatenating bang-bang (BB) control and decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced docoherence that result in quantum information dissipating into the environment. For the un-tunable qubit-qubit interaction in the quantum system, BB control plus DFSs encoding will stabilize encoded quantum states. We show how this quantum system to implement universal quantum computation.

Zhang, Y; Yu, B; Guo, G C; Zhang, Yong; Zhou, Zheng-Wei; Yu, Bo; Guo, Guang-Can

2004-01-01

407

Quantum computing of delocalization in small-world networks

We study a quantum small-world network with disorder and show that the system exhibits a delocalization transition. A quantum algorithm is built up which simulates the evolution operator of the model in a polynomial number of gates for exponential number of vertices in the network. The total computational gain is shown to depend on the parameters of the network and a larger than quadratic speed-up can be reached. We also investigate the robustness of the algorithm in presence of imperfections.

Giraud, O; Shepelyansky, D L

2005-01-01

408

Perturbative computation in a generalized quantum field theory

International Nuclear Information System (INIS)

We consider a quantum field theory that creates at any point of the space-time described by a q-deformed Heisenberg algebra which is interpreted as a phenomenological quantum theory describing the scattering of spin-O composed particles. We discuss the generation of Wick's expansion for this case and we compute perturbatively the scattering 1+2 ? 1'+2' to second order in the coupling constant. The result we find shows that the structure of a composed particle, described here phenomenologically by the deformed algebraic structure, can modify in a simple but non-trivial way the perturbation expansion for the process under consideration. (author)

409

Landau-Zener Transitions in an Adiabatic Quantum Computer

We report an experimental measurement of Landau-Zener transitions on an individual flux qubit within a multi-qubit superconducting chip designed for adiabatic quantum computation. The method used isolates a single qubit, tunes its tunneling amplitude Delta into the limit where Delta is much less than both the temperature T and the decoherence-induced energy level broadening, and forces it to undergo a Landau-Zener transition. We find that the behavior of the qubit agrees to a high degree of accuracy with theoretical predictions for Landau-Zener transition probabilities for a double-well quantum system coupled to 1/f magnetic flux noise.

Johansson, J; Berkley, A J; Bunyk, P; Choi, V; Harris, R; Johnson, M W; Lanting, T M; Lloyd, Seth; Rose, G

2008-01-01

410

NMR Quantum Computation with a hyperpolarized nuclear spin bulk

We consider two new quantum gate mechanisms based on nuclear spins in hyperp olarized solid $^{129}Xe$ and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) from hyperpolarized solid $^{129}Xe$ and HCl mixtures and optically pumped NMR in semiconductors. Such gates might be built up with particular spins addres sable based on MRI techniques and optical pumping and optical detection techniques. The schemes could be useful for implementing actual quantum computers in terms of a cellular automata architecture.

Luo, J; Luo, Jun; Zeng, Xizhi

1998-01-01

411

Many-body interactions with single-electron quantum dots for topological quantum computation

International Nuclear Information System (INIS)

We show that a many-body system of single-electron quantum dots, whose orbital states are dressed by a global magnetic field, can be described by an effective Hamiltonian with an anisotropic XZ spin-spin interaction which is proportional to the Zeeman splitting. We show that these interaction potentials give rise to spin-dependent Hubbard models with tunable nearest neighbor two-body and three-body interactions. The two-body interactions can even be switched off via the external electric field, and hence the three-body interaction plays a dominant role. The derivation of these effective interaction potentials follows from a well-controlled and systematic expansion into many-body interaction terms. Models of this type have appeared in the recent discussion of exotic quantum phases, in particular in the context of topological quantum phases and quantum computing, and we show that quantum dots can be regarded as a realistic experimental route which provides the basic building blocks and techniques toward the study of these phenomena. The main application of this derived model is to develop topological quantum computation.

412

Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.

Energy Technology Data Exchange (ETDEWEB)

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.__

Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George

2013-10-01

413

Topics in coherent state quantum computation and state purification

This dissertation discusses mainly transmission of coherent state qubits, generation of cat states, and entanglement purification of any stabilizer state. A quantum computer is any device for computation that makes direct use of distinctively quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. The elementary carriers in quantum computation and information are the quantum bits, or qubits. In contrast to classical bits, qubits can be in every superposition of the states |0> and |1>. This means that a vector describing a qubit may be any vector in a two dimensional Hilbert space. In this dissertation, we review a method for constructing a linear optical quantum computer using coherent states of light as the qubits, developed by Ralph, Gilchrist, Milburn, Munro, and Clancy. We show how an universal set of logic operations can be performed using coherent states, beam splitters, photon counters, and a source of superpositions of coherent state, called "cat states". We also discuss the principal source of errors for this scheme and then present this author's analysis of the behavior of teleportation or Z gate when a non-maximally entangled Bell state is used. We describe several different schemes to generate cat states and make an analysis of these schemes in a realistic experimental environment subject to problems such as photon loss, detector inefficiency, and limited strength of nonlinear interactions. Next, we consider that photon loss is the principal decoherence mechanism that affects a coherent-state based qubit transmission though a long optical fiber, and show how the errors introduced during transmission can be corrected in two different ways to encode the qubit. Lastly, we present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In this protocol, each party measures the stabilizer operators of an error correction code on his or her qubits, exchange their syndrome results, correct errors, and decode to obtain the desired purified state.

Vasconcelos, Hilma Helena Macedo De

414

Simple proof of equivalence between adiabatic quantum computation and the circuit model

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.

Mizel, A; Mitchell, M; Lidar, Daniel A.; Mitchell, Morgan; Mizel, Ari

2006-01-01

415

Simple proof of equivalence between adiabatic quantum computation and the circuit model.

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient. PMID:17930879

Mizel, Ari; Lidar, Daniel A; Mitchell, Morgan

2007-08-17

416

Quantum and classical parallelism in parity algorithms for ensemble quantum computers

International Nuclear Information System (INIS)

The determination of the parity of a string of N binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least N/2 oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor 2k, with k is a member of {{1,2,...,log2(N/2}}, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer

417

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. PMID:23938640

Wei, Hai-Rui; Deng, Fu-Guo

2013-07-29

418

Nanofabrication of multi-qubit solid state quantum computer device

International Nuclear Information System (INIS)

Full text: In the solid state quantum computer (SSQC) design proposed by Kane, an array of phosphorous-31 atoms embedded in a silicon substrate provides the quantum bits. Quantum information is encoded on the nuclear spin of these 31P atoms and interaction between the qubits is mediated via the donor electrons in a controlled way by employing surface gate electrodes. A critical requirement of this design is the alignment of the underlying 31P array to these gates and the single electron transistors (SETs) that facilitate the qubit readout. We report a fabrication method for scalable multi-qubit devices that allows accurate registration of metal SET and gate structures to the 31P qubits in a self aligned process which incorporates electron beam patterning, ion implantation and multi-angle metal evaporation

419

Is the brain a Clifford algebra quantum computer?

We propose a novel method to calculate invariants of colour and multicolour images. It employs an idea of classical and quantum hypercomplex numbers and combines it with the idea of classical and quantum number theoretical transforms over hypercomplex algebras, which reduce the computational complexity of the global recognition algorithm for nD k-multispectral images from O(knNn+1)to O(kNn log N) and to O(kn log N), respectively. Our hypotheses are 1) the brain of primates calculates hypercomplex-valued invariants of an image during recognizing, 2) visual systems of animals with different evolutionary history use different hypercomplex algebras. The main goal of the paper is to show that quantum Clifford algebras can be used to solve pattern recognition in multispectral environment in a natural and effective manner.

Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.

2001-11-01

420

Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_, 5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi, quant-ph/0110026]. The Letter claims an exponential speedup and reduction in error sensitivity, when phase-space density evolution under the Arnold cat map is performed on a quantum computer. On the one hand, some points have not yet been made by previous respondents. On the other, the authors' reaction [quant-ph/0110142] raises new issues. The present note addresses both.

Maasen van den Brink, A

2001-01-01

421

Fast read-out for semiconductor based quantum computation

International Nuclear Information System (INIS)

Full text: Quantum Computers promise unprecedented computational power for certain tasks if they can be scaled to large numbers of quantum bits (qubits). Systems with small numbers of qubits have already been demonstrated using ions in atom traps and small molecules in liquid NMR. However there is intense interest in quantum computer architectures, which can be scaled up to include many quantum bits. In an architecture proposed by Kane, the nuclear spin of 31P atoms embedded in silicon form the qubits, with operations on the qubits performed using gates located on the surface of the silicon. Along with the formidable technical challenge of creating a precise array of phosphorus atoms in silicon, one of the most significant difficulties is to read the spin state of the individual qubits. The difficulty is that the qubits must be well isolated from the external environment for the quantum computer to operate, yet it must also be possible to couple an external measurement system to read out each qubit at the end of the calculation. This talk will focus on the practical difficulties of reading out these spin-based qubits. We start by mapping the difficult problem of measuring a single nuclear spin on to the more tractable problem of measuring the movement of a single electron. This is achieved by transferring the nuclear spin state to the donor electron's spin state, and then detecting a spin-dependent tunnelling process between two closely spaced phosphorus donors. This single electron tunnelling event can then be detected with a nearby highly sensitive electrometer, such as a single electron transistor (SET). We have built a novel device to demonstrate this detection technique, and shown that single electron tunnelling in a coupled metal dot system can be observed non-invasively by correlating the output of two SETs. However, to be used in a spin-based quantum computer, readout must be performed on timescales shorter than the electron spin relaxation time, and I will discuss an extension of this scheme that allows detection of single charge transfers on microsecond timescales

422

Universal computation by multi-particle quantum walk

We show that multi-particle quantum walk is capable of universal quantum computation. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. As in a previous single-particle construction, we use a discrete version of scattering theory to establish universality. However, we use a different encoding of quantum data and exploit interactions between particles to implement two-qubit gates. In our scheme, an n-qubit circuit with g gates can be simulated by the dynamics of O(n) particles evolving for time poly(n,g) on a planar graph of maximum degree 4 with poly(n,g) vertices. Thus our graphs are exponentially smaller (as a function of n) than those used in the single-particle construction, offering the potential for efficient implementation by a system with a physical degree of freedom for each vertex of the graph. Our results apply to a broad class of multi-particle q...

Childs, Andrew M; Webb, Zak

2012-01-01

423

Numerical analysis of boosting scheme for scalable NMR quantum computation

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC’99) (ACM Press, New York, 1999), pp. 322-329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result—namely, that there is such a significant growth in the total binary entropy—disagrees with that of their analysis.

Saitoh, Akira; Kitagawa, Masahiro

2005-02-01

424

Silicon-based spin and charge quantum computation

Silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals due to the relatively long spin coherence times. For these spin qubits, donor electron charge manipulation by external gates is a key ingredient for control and read-out of single-qubit operations, while shallow donor exchange gates are frequently invoked to perform two-qubit operations. More recently, charge qubits based on tunnel coupling in P$_2^+$ substitutional molecular ions in Si have also been proposed. We discuss the feasibility of the building blocks involved in shallow donor quantum computation in silicon, taking into account the peculiarities of silicon electronic structure, in particular the six degenerate states at the conduction band edg...

Koiller, B; Capaz, R B; Martins, A S; Sarma, S D; Koiller, Belita; Hu, Xuedong

2005-01-01

425

Qudit quantum computation in the Jaynes-Cummings model

DEFF Research Database (Denmark)

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 sequences with more rapid numerically optimized sequences. In our third approach, we directly optimize the evolution of the system, without making use of any analytic techniques. While limited to smaller dimensional qudits, the third approach finds pulse sequences which carry out the desired gates in a time which is much shorter than either of the other two approaches.

Mischuck, Brian; MØlmer, Klaus

2013-01-01

426

Scalable register initialization for quantum computing in an optical lattice

International Nuclear Information System (INIS)

The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunnelling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the centre which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling can sustain a commensurately filled register for the duration of a quantum computation

427

Scalable register initialization for quantum computing in an optical lattice

Energy Technology Data Exchange (ETDEWEB)

The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattic