Li, Shu-Shen; Long, Gui-Lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization.
Kiili, Markus
1997-01-01
The aim of this thesis was to explain what quantum computing is. The information for the thesis was gathered from books, scientific publications, and news articles. The analysis of the information revealed that quantum computing can be broken down to three areas: theories behind quantum computing explaining the structure of a quantum computer, known quantum algorithms, and the actual physical realizations of a quantum computer. The thesis reveals that moving from classical memor...
Steane, A M
1998-01-01
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and qua...
Quantum Chaos & Quantum Computers
D. L. Shepelyansky
2000-01-01
The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergod...
Berthiaume, A.
1998-01-01
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool. This review is about to tell the story of theoretical quantum computation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum ...
Aharonov, D
1998-01-01
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool. This review is about to tell the story of theoretical quantum computation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantum computers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained. I w...
Quantum computers and quantum computations
Energy Technology Data Exchange (ETDEWEB)
Valiev, Kamil' A [Institute of Physics and Technology, Russian Academy of Sciences, Moscow (Russian Federation)
2005-01-31
This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review. (reviews of topical problems)
International Nuclear Information System (INIS)
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource. It turns out that 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 depar
Scarani, Valerio
1998-01-01
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.
Eisert, J.; Wolf, M. M.
2004-01-01
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).
Unconventional Quantum Computing Devices
Lloyd, Seth
2000-01-01
This paper investigates a variety of unconventional quantum computation devices, including fermionic quantum computers and computers that exploit nonlinear quantum mechanics. It is shown that unconventional quantum computing devices can in principle compute some quantities more rapidly than `conventional' quantum computers.
Quantum information and computation
Bub, Jeffrey
2005-01-01
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.
International Nuclear Information System (INIS)
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer
Energy Technology Data Exchange (ETDEWEB)
Kendon, Viv [School of Physics and Astronomy, University of Leeds, LS2 9JT (United Kingdom)
2014-12-04
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.
Quantum Computational Complexity
Watrous, John
2008-01-01
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of quantum complexity classes based on these notions, such as BQP, QMA, and QIP, are presented. Other topics in quantum complexity, including quantum advice, space-bounded quantum computation, and bounded-depth quantum circuits, are also discussed.
Quantum Robots and Quantum Computers
Benioff, Paul
1997-01-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and 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 environments. Some propert...
Automata and Quantum Computing
Ambainis, Andris; Yakaryilmaz, Abuzer
2015-01-01
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers.
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
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
Quantum Computing for Computer Architects
Metodi, Tzvetan
2011-01-01
Quantum computers can (in theory) solve certain problems far faster than a classical computer running any known classical algorithm. While existing technologies for building quantum computers are in their infancy, it is not too early to consider their scalability and reliability in the context of the design of large-scale quantum computers. To architect such systems, one must understand what it takes to design and model a balanced, fault-tolerant quantum computer architecture. The goal of this lecture is to provide architectural abstractions for the design of a quantum computer and to explore
Lloyd, Seth
2000-01-01
Necessary and sufficient conditions are given for the construction of a hybrid quantum computer that operates on both continuous and discrete quantum variables. Such hybrid computers are shown to be more efficient than conventional quantum computers for performing a variety of quantum algorithms, such as computing eigenvectors and eigenvalues.
Quantum robots and quantum computers
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Directory of Open Access Journals (Sweden)
Prashant Anil Patil
2012-04-01
Full Text Available This paper gives the detailed information about Quantum computer, and difference between quantum computer and traditional computers, the basis of Quantum computers which are slightly similar but still different from traditional computer. Many research groups are working towards the highly technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. Quantum computer is very much use full for computation purpose in field of Science and Research. Large amount of data and information will be computed, processing, storing, retrieving, transmitting and displaying information in less time with that much of accuracy which is not provided by traditional computers.
Quantum Computation via Paraconsistent Computation
Agudelo, Juan C.; Carnielli, Walter
2006-01-01
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum computation: quantum Turing machines and quantum circuits, and revise quantum algorithms to solve the so-called Deutsch's problem and Deutsch-Jozsa problem. Then, we show the potentialities of the PTMs model of computation simulating the presented q...
Kendon, Vivien M; Munro, William J
2010-01-01
We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data is encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data is encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue compute...
Integrable Quantum Computation
Zhang, Yong
2011-01-01
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.
Quantum Computers and Quantum Coherence
DiVincenzo, D. P.; Loss, D.
1999-01-01
If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information processing, showing that the famous Shor speedup of integer factoring is just one of a host of important applications for qubits, including cryptography, counterfeit protection, channel capacity enhancement, distributed computing, and others. We review our pr...
Patel, A D
1999-01-01
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is it to make a quantum computer? I summarise some of the important concepts of quantum computation, in an attempt to answer these questions. A deeper
Quantum Computers and Quantum Coherence
Di Vincenzo, D P
1999-01-01
If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information processing, showing that the famous Shor speedup of integer factoring is just one of a host of important applications for qubits, including cryptography, counterfeit protection, channel capacity enhancement, distributed computing, and others. We review our proposed spin-quantum dot architecture for a quantum computer, and we indicate a variety of first generation materials, optical, and electrical measurements which should be considered. We analyze the efficiency of a two-dot device as a transmitter of quantum information via the ballistic propagation of carriers in a Fermi sea.
DiVincenzo, David P.
1996-01-01
I provide an introduction to quantum computers, describing how they might be realized using language accessible to a solid state physicist. A listing of the minimal requirements for creating a quantum computer is given. I also discuss several recent developments in the area of quantum error correction, a subject of importance not only to quantum computation, but also to some aspects of the foundations of quantum theory.
Searching with Quantum Computers
Grover, Lov K.
2000-01-01
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
Quantum mechanics and computation
International Nuclear Information System (INIS)
We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs
Introduction to Quantum Computation
Ekert, A.
A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.
Kendon, Vivien M; Nemoto, Kae; Munro, William J
2010-08-13
We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future. PMID:20603371
Introduction to quantum computers
Berman, Gennady P; Mainieri, Ronnie; Tsifrinovich, Vladimir I
1998-01-01
Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shorâ€™s algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by im
Algorithms for Quantum Computers
Smith, Jamie; Mosca, Michele
2010-01-01
This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of quantum Fourier transform based algorithms, followed by quantum searching and some of its early generalizations. It continues with a more in-depth description of two more recent developments: algorithms developed in the quantum walk paradigm, followed by tenso...
Scalable optical quantum computer
International Nuclear Information System (INIS)
A way of designing a scalable optical quantum computer based on the photon echo effect is proposed. Individual rare earth ions Pr3+, regularly located in the lattice of the orthosilicate (Y2SiO5) crystal, are suggested to be used as optical qubits. Operations with qubits are performed using coherent and incoherent laser pulses. The operation protocol includes both the method of measurement-based quantum computations and the technique of optical computations. Modern hybrid photon echo protocols, which provide a sufficient quantum efficiency when reading recorded states, are considered as most promising for quantum computations and communications. (quantum computer)
Scalable optical quantum computer
Energy Technology Data Exchange (ETDEWEB)
Manykin, E A; Mel' nichenko, E V [Institute for Superconductivity and Solid-State Physics, Russian Research Centre ' Kurchatov Institute' , Moscow (Russian Federation)
2014-12-31
A way of designing a scalable optical quantum computer based on the photon echo effect is proposed. Individual rare earth ions Pr{sup 3+}, regularly located in the lattice of the orthosilicate (Y{sub 2}SiO{sub 5}) crystal, are suggested to be used as optical qubits. Operations with qubits are performed using coherent and incoherent laser pulses. The operation protocol includes both the method of measurement-based quantum computations and the technique of optical computations. Modern hybrid photon echo protocols, which provide a sufficient quantum efficiency when reading recorded states, are considered as most promising for quantum computations and communications. (quantum computer)
'Photosynthetic' Quantum Computers?
Hitchcock, Scott M.
2001-01-01
Do quantum computers already exist in Nature? It is proposed that they do. Photosynthesis is one example in which a 'quantum computer' component may play a role in the 'classical' world of complex biological systems. A 'translation' of the standard metabolic description of the 'front-end' light harvesting complex in photosynthesis into the language of quantum computers is presented. Biological systems represent an untapped resource for thinking about the design and operation of hybrid quantum...
Quantum computation as geometry.
Nielsen, Michael A; Dowling, Mark R; Gu, Mile; Doherty, Andrew C
2006-02-24
Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers. PMID:16497928
Quantum computer games: quantum minesweeper
Gordon, Michal; Gordon, Goren
2010-07-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical minesweeper the goal of the game is to discover all the mines laid out on a board without triggering them, in the quantum version there are several classical boards in superposition. The goal is to know the exact quantum state, i.e. the precise layout of all the mines in all the superposed classical boards. The player can perform three types of measurement: a classical measurement that probabilistically collapses the superposition; a quantum interaction-free measurement that can detect a mine without triggering it; and an entanglement measurement that provides non-local information. The application of the concepts taught by quantum minesweeper to one-way quantum computing are also presented.
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)
Vedral, V; Vedral, Vlatko; Plenio, Martin B.
1998-01-01
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic principles of quantum computation, including the construction of basic gates, and networks. We illustrate the power of quantum algorithms using the simple problem of Deutsch, and explain, again in very simple terms, the well known algorithm of Shor for factorisation of large numbers into primes. We then describe physical implementations of quantum computers, focusing on one in particular, the linear ion-trap realization. We explain that the main obstacle to building an actual quantum computer is the problem of decoherence, which we show may be circumvented using the methods of quantum error correction.
Fujii, Toshiyuki; Hatakenaka, Noriyuki
2009-01-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e., joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Preskill, J
1997-01-01
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 10^6 qubits, with a probability of error per quantum gate of order 10^{-6}, would be a formidable factoring engine. Even a smaller, less accurate quantum computer would be able to perform many useful tasks. (This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18 December 1996.)
Quantum Computing since Democritus
Aaronson, Scott
2013-03-01
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.
Quantum Computers and Dissipation
Palma, G. Massimo; Suominen, Kalle-Antti; Ekert, Artur K.
1997-01-01
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.
Quantum Computers and Dissipation
Palma, G M; Ekert, A K; Suominen, Kalle-Antti; Ekert, Artur K.
1996-01-01
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.
Quantum computing classical physics
Meyer, David A.
2001-01-01
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice gas automata--and show how to implement them efficiently on standard quantum computers.
Energy Technology Data Exchange (ETDEWEB)
Knill, E.; Laflamme, R.; Zurek, W.H. [Los Alamos National Lab., NM (United States)
1998-01-16
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.
Barenco, Adriano
1996-01-01
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit quantum features could factor large composite integers. This task is believed to be out of reach of classical computers as soon as the number of digits in the number to factor exceeds a certain limit. The additional power of quantum computers comes from the po...
Quantum Computing Without Entanglement
Biham, Eli; Brassard, Gilles; Kenigsberg, Dan; Mor, Tal
2003-01-01
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a xed number of oracle calls. Using a separable (that is, unentangled) n-qubit state, we show that the Deutsch-Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best pos...
Scalable optical quantum computer
Manykin, E. A.; Mel'nichenko, E. V.
2014-12-01
A way of designing a scalable optical quantum computer based on the photon echo effect is proposed. Individual rare earth ions Pr3+, regularly located in the lattice of the orthosilicate (Y2SiO5) crystal, are suggested to be used as optical qubits. Operations with qubits are performed using coherent and incoherent laser pulses. The operation protocol includes both the method of measurement-based quantum computations and the technique of optical computations. Modern hybrid photon echo protocols, which provide a sufficient quantum efficiency when reading recorded states, are considered as most promising for quantum computations and communications.
Lanzagorta, Marco
2009-01-01
In this text we present a technical overview of the emerging field of quantum computation along with new research results by the authors. What distinguishes our presentation from that of others is our focus on the relationship between quantum computation and computer science. Specifically, our emphasis is on the computational model of quantum computing rather than on the engineering issues associated with its physical implementation. We adopt this approach for the same reason that a book on computer programming doesn't cover the theory and physical realization of semiconductors. Another distin
Explorations in quantum computing
Williams, Colin P
2011-01-01
By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. ""Quantum computing"" is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers -- and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking suppos
Quantum Computation with Quantum Dots
Loss, D; Loss, Daniel; Vincenzo, David P. Di
1998-01-01
We propose the implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a newly derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments which would provide an initial demonstration of the desired non-equilibrium spin dynamics are proposed.
Dissipative quantum computing with open quantum walks
International Nuclear Information System (INIS)
An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates
Dissipative quantum computing with open quantum walks
Energy Technology Data Exchange (ETDEWEB)
Sinayskiy, Ilya; Petruccione, Francesco [National Institute for Theoretical Physics and Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban (South Africa)
2014-12-04
An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.
Duality and Recycling Computing in Quantum Computers
Long, Gui Lu; Liu, Yang
2007-01-01
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 pass...
Preskill, John
1997-01-01
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be perf...
Vlasov, Alexander Yu.
2004-01-01
In the paper is considered stairway-like design of quantum computer, i.e., array of double quantum dots or wells. The model is quite general to include wide variety of physical systems from coupled quantum dots in experiments with solid state qubits, to very complex one, like DNA molecule. At the same time it is concrete enough, to describe main physical principles for implementation of universal set of quantum gates, initialization, measurement, decoherence, etc.
Ekert, A K; Hayden, P; Inamori, H; Jones, J A; Oi, D K L; Vedral, V
2000-01-01
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.
Quantum computing hamiltonian cycles
Rudolph, T
1996-01-01
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths originating from a chosen vertex, and furthermore to subsequently project out all states not corresponding to Hamiltonian cycles.
Zak, M.
1998-01-01
Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.
Quantum Computational Fuzzy Logics
BERTINI, CESARINO; LEPORINI, ROBERTO
2007-01-01
The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of info...
Chuang, I.L.; Yamamoto, Y.
1995-01-01
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...
High Performance Quantum Computing
Devitt, Simon J.; Munro, William J.; Nemoto, Kae
2008-01-01
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...
Quantum computing with trapped ions
Haeffner, H.; C. F. Roos; Blatt, R.
2008-01-01
Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.
Instantaneous Quantum Computation
Shepherd, Dan
2008-01-01
We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here instantaneous quantum computation because it allows for essentially no temporal structure within the quantum dynamics. Using the theory of binary matroids, we argue that the paradigm is rich enough to enable sampling from probability distributions that cannot, classically, be sampled from efficiently and accurately. This paradigm also admits simple interactive proof games that may convince a skeptic of the existence of truly quantum effects. Furthermore, these effects can be created using significantly fewer qubits than are required for running Shor's Algorithm.
International Nuclear Information System (INIS)
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
Quantum computing with trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, R.J.
1998-01-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
Finkelstein, David Ritz
2012-01-01
Set theory reduces all processes to assembly and disassembly. A similar architecture is proposed for nature as quantum computer. It resolves the classical space-time underlying Feynman diagrams into a quantum network of creation and annihilation processes, reducing kinematics to quantum statistics, and regularizing the Lie algebra of the Einstein diffeomorphism group. The usually separate and singular Lie algebras of kinematics, statistics, and conserved currents merge into one regular statistics Lie algebra.
Efficient Distributed Quantum Computing
Beals, Robert; Brierley, Stephen; Gray, Oliver; Harrow, Aram; Kutin, Samuel; Linden, Noah; Shepherd, Dan; Stather, Mark
2012-01-01
We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the circuit model can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit. In addition, we apply our results to existing memory intensive quantum algorithms. We present a par...
Parallel Quantum Computing in a Single Ensemble Quantum Computer
Long, Gui Lu; Xiao, Li
2003-01-01
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 ...
International Nuclear Information System (INIS)
This paper reports that current conceptions of quantum mechanical computers inherit from conventional digital machines two apparently interacting features, machine imperfection and temporal development of the computational process. On account of machine imperfection, the process would become ideally reversible only in the limiting case of zero speed. Therefore the process is irreversible in practice and cannot be considered to be a fundamental quantum one. By giving up classical features and using a linear, reversible and non-sequential representation of the computational process - not realizable in classical machines - the process can be identified with the mathematical form of a quantum steady state. This form of steady quantum computation would seem to have an important bearing on the notion of cognition
Entanglement and Quantum Computation
Jozsa, R
1997-01-01
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.
Using Quantum Computers for Quantum Simulation
Kendon, Vivien M.; Brown, Katherine L.; Munro, William J
2010-01-01
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beg...
Towards Quantum Computational Logics
Ledda, Antonio; Sergioli, Giuseppe
2010-12-01
Quantum computational logics have recently stirred increasing attention (Cattaneo et al. in Math. Slovaca 54:87-108, 2004; Ledda et al. in Stud. Log. 82(2):245-270, 2006; Giuntini et al. in Stud. Log. 87(1):99-128, 2007). In this paper we outline their motivations and report on the state of the art of the approach to the logic of quantum computation that has been recently taken up and developed by our research group.
Pinski, Sebastian D.
2011-01-01
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small pr...
Computational Methods for Simulating Quantum Computers
De Raedt, H.; Michielsen, K.
2004-01-01
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation software for ideal and physical models of quantum computers.
An Introduction to Quantum Computers
Zalka, Christof
1998-01-01
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding lengthy discussions.
Quantum Computing: a Quantum Group Approach
Wang, Zhenghan
2013-01-01
There is compelling theoretical evidence that quantum physics will change the face of information science. Exciting progress has been made during the last two decades towards the building of a large scale quantum computer. A quantum group approach stands out as a promising route to this holy grail, and provides hope that we may have quantum computers in our future.
Ramelow, S; Steinberg, A M; White, A G
2009-01-01
In the circuit model, quantum computers rely on the availability of a universal quantum gate set. A particularly intriguing example of such a set is the "matchgates" along with swap, the simple exchange of two qubits. In this paper, we show a simple decomposition of arbitrary matchgates into better known elementary gates, and implement one matchgate in a linear optics experiment using single photons. We characterize the gate performance via quantum process tomography and represent the resulting quantum process in a novel way, as a fidelity map in the space of all possible nonlocal two-qubit unitaries. In addition, we propose a new non-local, diagnostic process measure.
Energy Technology Data Exchange (ETDEWEB)
Jones, Jonathan [Oxford University (United Kingdom)
2002-04-01
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.)
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.)
Quantum Computation The Ultimate Frontier
Adami, C; Adami, Chris; Dowling, Jonathan P.
2002-01-01
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many different quantum systems are being explored for their suitability to serve as a physical substrate for the quantum computer of the future. I discuss some of the theoretical foundations of quantum computer science, including algorithms and error correction, and present a few physical systems that have shown promise as a quantum computing platform. Finally, we discuss a spin-off of the quantum computing revolution: quantum technologies.
Using Quantum Computers for Quantum Simulation
Directory of Open Access Journals (Sweden)
Vivien M. Kendon
2010-11-01
Full Text Available Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.
Using Quantum Computers for Quantum Simulation
Brown, Katherine L; Kendon, Vivien M
2010-01-01
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with less than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we provide a review of the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.
An Introduction to Quantum Computing
Yanofsky, Noson S.
2007-01-01
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 dimensional) quan...
Quantum Computers and Quantum Computer Languages: Quantum Assembly Language and Quantum C Language
Blaha, Stephen
2002-01-01
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
International Nuclear Information System (INIS)
We discuss the notion of quantum computational webs: These are quantum states universal for measurement-based computation, which can be built up from a collection of simple primitives. The primitive elements--reminiscent of building blocks in a construction kit--are (i) one-dimensional states (computational quantum wires) with the power to process one logical qubit and (ii) suitable couplings, which connect the wires to a computationally universal web. All elements are preparable by nearest-neighbor interactions in a single pass, of the kind accessible in a number of physical architectures. We provide a complete classification of qubit wires, a physically well-motivated class of universal resources that can be fully understood. Finally, we sketch possible realizations in superlattices and explore the power of coupling mechanisms based on Ising or exchange interactions.
Pinski, Sebastian D
2011-01-01
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.
Spintronics and Quantum Computing with Quantum Dots
Recher, P.; Loss, D.; Levy, J.
2000-01-01
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 ...
I, Quantum Robot: Quantum Mind control on a Quantum Computer
zizzi, Paola
2008-01-01
The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A way toward the realization of intelligent quantum robots is to adopt a quantum metalanguage to control quantum robots. A physical implementation of a quantum metalanguage might be the use of coherent states in brain signals.
Simulating quantum mechanics on a quantum computer
Boghosian, B M; Boghosian, Bruce M.; Taylor, Washington
1998-01-01
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac and gauge particles are discussed.
Simulating Chemistry Using Quantum Computers
Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alan
2011-01-01
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achi...
Quantum entanglement, quantum communication and the limits of quantum computing
Ambainis, Andris
Quantum entanglement is a term describing the quantum correlations between different parts of a quantum system. Quantum information theory has developed sophisticated techniques to quantify and study quantum entanglement. In this thesis, we show how to apply those techniques to problems in quantum algorithms, complexity theory, communication and cryptography. The main results are: (1) quantum communication protocols that are exponentially more efficient that conventional (classical) communication protocols, (2) unconditionally secure quantum protocols for cryptographic problems, (3) a new "quantum adversary" method for proving lower bounds on quantum algorithms, (4) a study of "one clean qubit computation", a model related to the experimental implementation of quantum computers using NMR (nucleo-magnetic resonance) technology.
Quantum++ - A C++11 quantum computing library
Gheorghiu, Vlad
2014-01-01
Quantum++ is a general-purpose multi-threaded quantum computing library written in C++11 and composed solely of header files. The library is not restricted to qubit systems or specific quantum information processing tasks, being capable of simulating arbitrary quantum processes. The main design factors taken in consideration were ease of use, portability, and performance.
Quantum information and computation
International Nuclear Information System (INIS)
During the past two decades, there has emerged the new subject of quantum information and computation which both offers the possibility of powerful new modes of computing and communication and also suggests deep links between the well established disciplines of quantum theory and information theory and computer science. In recent years, the growth of the subject has been explosive, with significant progress in theory and experiment. The area has a highly interdisciplinary character with contributions from physicists, mathematicians and computer scientists in particular. Developments have occurred in diverse areas including quantum algorithms, quantum communication, quantum cryptography, entanglement and nonlocality. This progress has been reflected in contributions to Journal of Physics A: Mathematical and General which traditionally provides a natural home for this area of research. Furthermore, the journal's commitment to this field has recently been strengthened by the appointments of Sandu Popescu and Nicolas Gisin to the Editorial Board, and in this special issue we take the opportunity to present a snapshot of the present state of the art. (author)
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
Topologically protected quantum computation
Wootton, James R; Doucot, Benoit; Pachos, Jiannis K
2009-01-01
We propose a novel fault-tolerant scheme for quantum computation based on the topological phase of a spin lattice model. Abelian anyons are used to simulate non-Abelian properties relevant to topological quantum computation. Universality is realized by using anyon transport and single spin measurements. Along with the topological nature of the encoding, logical states are protected from thermal excitations by a finite energy gap. A proof of principle scheme is proposed that can be realized in Josephson junctions with state of the art technology.
Landahl, Andrew
2012-10-01
Quantum computers promise to exploit counterintuitive quantum physics principles like superposition, entanglement, and uncertainty to solve problems using fundamentally fewer steps than any conventional computer ever could. The mere possibility of such a device has sharpened our understanding of quantum coherent information, just as lasers did for our understanding of coherent light. The chief obstacle to developing quantum computer technology is decoherence--one of the fastest phenomena in all of physics. In principle, decoherence can be overcome by using clever entangled redundancies in a process called fault-tolerant quantum error correction. However, the quality and scale of technology required to realize this solution appears distant. An exciting alternative is a proposal called ``adiabatic'' quantum computing (AQC), in which adiabatic quantum physics keeps the computer in its lowest-energy configuration throughout its operation, rendering it immune to many decoherence sources. The Adiabatic Quantum Architectures In Ultracold Systems (AQUARIUS) Grand Challenge Project at Sandia seeks to demonstrate this robustness in the laboratory and point a path forward for future hardware development. We are building devices in AQUARIUS that realize the AQC architecture on up to three quantum bits (``qubits'') in two platforms: Cs atoms laser-cooled to below 5 microkelvin and Si quantum dots cryo-cooled to below 100 millikelvin. We are also expanding theoretical frontiers by developing methods for scalable universal AQC in these platforms. We have successfully demonstrated operational qubits in both platforms and have even run modest one-qubit calculations using our Cs device. In the course of reaching our primary proof-of-principle demonstrations, we have developed multiple spinoff technologies including nanofabricated diffractive optical elements that define optical-tweezer trap arrays and atomic-scale Si lithography commensurate with placing individual donor atoms with scanning-tunneling microscopy. I will review our experimental and theoretical progress in this plenary talk.[4pt] This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Undergraduate computational physics projects on quantum computing
Candela, D.
2015-08-01
Computational projects on quantum computing suitable for students in a junior-level quantum mechanics course are described. In these projects students write their own programs to simulate quantum computers. Knowledge is assumed of introductory quantum mechanics through the properties of spin 1/2. Initial, more easily programmed projects treat the basics of quantum computation, quantum gates, and Grover's quantum search algorithm. These are followed by more advanced projects to increase the number of qubits and implement Shor's quantum factoring algorithm. The projects can be run on a typical laptop or desktop computer, using most programming languages. Supplementing resources available elsewhere, the projects are presented here in a self-contained format especially suitable for a short computational module for physics students.
An Introduction to Quantum Computing
Yanofsky, Noson S
2007-01-01
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 dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.
Quantum Computations: Fundamentals and Algorithms
International Nuclear Information System (INIS)
Basic concepts of quantum information theory, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are concerned. The main blocks of quantum logic, schemes of quantum calculations implementation, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are presented here. Among them special place is taken by Shor's algorithm of number factorization and Grover's algorithm of unsorted database search. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum errors correction are described
Demonstration of blind quantum computing.
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip
2012-01-20
Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available. PMID:22267806
Preskill, J
1997-01-01
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 ...
Quantum Computation and Spin Physics
DiVincenzo, David P.
1996-01-01
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.
Quantum Nondemolition Monitoring of Universal Quantum Computers
Ozawa, Masanao
1997-01-01
The halt scheme for quantum Turing machines, originally proposed by Deutsch, is reformulated precisely and is proved to work without spoiling the computation. The ``conflict'' pointed out recently by Myers in the definition of a universal quantum computer is shown to be only apparent. In the context of quantum nondemolition (QND) measurement, it is also shown that the output observable, an observable representing the output of the computation, is a QND observable and that the halt scheme is e...
Quantum Computation toward Quantum Gravity
Zizzi, P A
2001-01-01
The aim of this paper is to enlight the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. Here we present the quantum version of the holographic principle by considering each pixel of area of an event horizon as a qubit. This is possible if the horizon is pierced by spin networks' edges of spin 1\\2, in t...
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.
Relativistic quantum chemistry on quantum computers
Veis, Libor; Viš?ák, Jakub; Fleig, Timo; Knecht, Stefan; Saue, Trond; Visscher, Lucas; Pittner, Ji?í
2012-03-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only the nonrelativistic regime (i.e., the Schrödinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-not (cnot) gates, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization.
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.
Notes on Adiabatic Quantum Computers
Tamir, Boaz; Cohen, Eliahu
2015-01-01
We discuss the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong relations between the three. We conclude with a brief presentation of the D-Wave computer and some future challenges.
Arrighi, P; Arrighi, Pablo; Salvail, Louis
2003-01-01
We investigate the possibility of having someone carry out the work of executing a function for you, but without letting him learn anything about your input. Say Alice wants Bob to compute some well-known function f upon her input x, but wants to prevent Bob from learning anything about x. The situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute f(x) "blindly", i.e. without observing x? We provide such a blind computation protocol for the class of functions which admit an efficient procedure to generate random input-output pairs, e.g. factorization. The setting is quantum, the security is unconditional, the eavesdropper is as malicious as can be. Keywords: Secure Circuit Evaluation, Secure Two-party Computation, Information Hiding, Information gain vs disturbance.
Bellac, Michel Le
2014-11-01
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.
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
Programmable architecture for quantum computing :
Chen, J.; WANG, L; Charbon, E.; Wang, B
2013-01-01
A programmable architecture called “quantum FPGA (field-programmable gate array)” (QFPGA) is presented for quantum computing, which is a hybrid model combining the advantages of the qubus system and the measurement-based quantum computation. There are two kinds of buses in QFPGA, the local bus and 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)....
Vibrational coherent quantum computation
Paternostro, M; Knight, P L; Paternostro, Mauro
2005-01-01
A long-lived coherent state and non-linear interaction have been experimentally demonstrated for the vibrational mode of a trapped ion. We propose an implementation of quantum computation using coherent states of the vibrational modes of trapped ions. Differently from earlier experiments, we consider a far-off resonance for the interaction between external fields and the ion in a bidimensional trap. By appropriate choices of the detunings between the external fields, the adiabatic elimination of the ionic excited level from the Hamiltonian of the system allows for beam splitting between orthogonal vibrational modes, production of coherent states and non-linear interactions of various kinds. In particular, this model enables the generation of the four coherent Bell states. Furthermore, all the necessary operations for quantum computation such as preparation of qubits, one-qubit and controlled two-qubit operations, are possible. The detection of the state of a vibrational mode in a Bell state is made possible b...
Quantum Computation vs. Firewalls
Harlow, Daniel
2013-01-01
In this paper we discuss quantum computational restrictions on the types of thought experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the smoothness of black hole horizons. We argue that the quantum computations required to do these experiments take a time which is exponential in the entropy of the black hole under study, and we show that for a wide variety of black holes this prevents the experiments from being done. We interpret our results as motivating a broader type of non-locality than is usually considered in the context of black hole thought experiments, and claim that once this type of non-locality is allowed there is no need for firewalls. Our results do not threaten the unitarity of of black hole evaporation or the ability of advanced civilizations to test it.
Quantum Gravity on a Quantum Computer?
Kempf, Achim
2013-01-01
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.
Quantum Gravity on a Quantum Computer?
Kempf, Achim
2014-05-01
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.
Genetic Algorithms and Quantum Computation
Giraldi, Gilson A.; Portugal, Renato; Thess, Ricardo N.
2004-01-01
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so called Quantum Evolutionary Programming has two major sub-areas: Quantum Inspired Genetic Algorithms (QIGAs) and Quantum Genetic Algorithms (QGAs). The former adopts qubit chromosomes as representations and employs quantum gates for the s...
New Trends in Quantum Computing
Brassard, Gilles
1996-01-01
Classical and quantum information are very different. Together they can perform feats that neither could achieve alone, such as quantum computing, quantum cryptography and quantum teleportation. Some of the applications range from helping to preventing spies from reading private communications. Among the tools that will facilitate their implementation, we note quantum purification and quantum error correction. Although some of these ideas are still beyond the grasp of current technology, quan...
Relativistic quantum chemistry on quantum computers
Veis, Libor; Viš?ák, Jakub; Fleig, Timo; Knecht, Stefan; Saue, Trond; Visscher, Lucas; Pittner, Ji?í
2011-01-01
Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations have been reported. However, so far only the non-relativistic regime (i.e. Schroedinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. In this letter we present the first quantum algorithm ...
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.; Knecht, S.; Saue, T.; Visscher, L.; Pittner, J.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic ...
Spin-Based Quantum Dot Quantum Computing
Hu, Xuedong
2004-01-01
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.
Quantum computing of semiclassical formulas.
Georgeot, B; Giraud, O
2008-04-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases. PMID:18517721
Embedding classical into quantum computation
Jozsa, Richard
2008-01-01
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits (Valiant's theorem) appear as two special cases. Viewing these simulatable classes as subsets of the space of all quantum computations, we may consider minimal extensions that suffice to regain full quantum computational power, which provides an approach to exploring the efficacy of quantum over classical computation.
Quantum computing of semiclassical formulas
Georgeot, Bertrand; Giraud, Olivier
2008-01-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
DEFF Research Database (Denmark)
Salvail, Louis; Arrighi, Pablo
2006-01-01
We investigate the possibility of "having someone carry out the work of executing a function for you, but without letting him learn anything about your input". Say Alice wants Bob to compute some known function f upon her input x, but wants to prevent Bob from learning anything about x. The...... situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute f(x) "blindly", i.e. without observing x? We provide such a blind computation...... protocol for the class of functions which admit an efficient procedure to generate random input-output pairs, e.g. factorization. The cheat-sensitive security achieved relies only upon quantum theory being true. The security analysis carried out assumes the eavesdropper performs individual attacks....
Quantum buses and quantum computer architecture based on quantum dots
D'Amico, I
2005-01-01
We propose a quantum computer architecture based on quantum dots both for short distance and for long distance communication/computation. Our scheme exploits the natural characteristics of self-assembled quantum dots and it is scalable. It is centered on the idea of a quantum bus based on semiconductor self-assembled quantum dots. This allows for transmission of qubits between the different quantum registers, and could be integrated in most of the present proposal for semiconductor quantum dot-based quantum computation. Our proposal exploits the peculiar properties of {\\it relatively short} spin-chains, and advantages and disadvantages of two possible implementations, both based on spin-chain global dynamics, are discussed in details. A clear advantage of the scheme is to avoid the use of microcavities for long distance communication between different elements of the quantum computer. In this respect our scheme is comparatively faster than hybrid quantum dot-microcavity schemes.
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.; Knecht, S.; Saue, T.; Visscher, L.; Pittner, J.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only the...... nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...
Quantum computing on encrypted data
Fisher, K. A. G.; Broadbent, A.; Shalm, L. K.; Yan, Z.; Lavoie, J.; Prevedel, R.; Jennewein, T.; Resch, K. J.
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Decoherence in adiabatic quantum computation
Albash, Tameem; Lidar, Daniel A.
2015-06-01
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master-equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed-system setting, remain beneficial in the open-system setting. To address the high computational cost of master-equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.
Quantum computing with defects
Weber, J R; Varley, J B; Janotti, A; Buckley, B B; Van de Walle, C G; Awschalom, D D
2010-01-01
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...
Energy Dissipation in Quantum Computers
Granik, A.; Chapline, G.
2003-01-01
A method is described for calculating the heat generated in a quantum computer due to loss of quantum phase information. Amazingly enough, this heat generation can take place at zero temperature. and may explain why it is impossible to extract energy from vacuum fluctuations. Implications for optical computers and quantum cosmology are also briefly discussed.
Communication Capacity of Quantum Computation
Bose, S; Vedral, V
2000-01-01
By considering quantum computation as a communication process, we relate its efficiency to a communication capacity. This formalism allows us to rederive lower bounds on the complexity of search algorithms. It also enables us to link the mixedness of a quantum computer to its efficiency. We discuss the implications of our results for quantum measurement.
Quantum computation and complexity theory
Svozil, K.
1994-01-01
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.
Vibrational coherent quantum computation
International Nuclear Information System (INIS)
A long-lived coherent state and nonlinear interaction have been experimentally demonstrated for the vibrational mode of a trapped ion. We propose an implementation of quantum computation using coherent states of the vibrational modes of trapped ions. Differently from earlier experiments, we consider a far-off resonance for the interaction between external fields and the ion in a bidimensional trap. By appropriate choices of the detunings between the external fields, the adiabatic elimination of the ionic excited level from the Hamiltonian of the system allows for beam splitting between orthogonal vibrational modes, production of coherent states, and nonlinear interactions of various kinds. In particular, this model enables the generation of the four coherent Bell states. Furthermore, all the necessary operations for quantum computation, such as preparation of qubits and one-qubit and controlled two-qubit operations, are possible. The detection of the state of a vibrational mode in a Bell state is made possible by the combination of resonant and off-resonant interactions between the ion and some external fields. We show that our read-out scheme provides highly efficient discrimination between all the four Bell states. We extend this to a quantum register composed of many individually trapped ions. In this case, operations on two remote qubits are possible through a cavity mode. We emphasize that our remote-qubit operation scheme does not require a high-quality factor resonator: the cavity field acts as a catalyst for the gate operation
Quantum computer for dummies (in Russian)
Grozin, Andrey
2011-01-01
An introduction (in Russian) to quantum computers, quantum cryptography, and quantum teleportation for students who have no previous knowledge of these subjects, but know quantum mechanics. Several simple examples are considered in detail using the quantum computer emulator QCL.
Quantum computing with mixed states
Siomau, Michael; Fritzsche, Stephan
2011-01-01
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits.
Energy Technology Data Exchange (ETDEWEB)
Breuer, Reinhard (comp.)
2010-07-01
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)
Interactive Proofs For Quantum Computations
Aharonov, Dorit; Eban, Elad
2008-01-01
It is generally accepted that large quantum systems cannot be simulated efficiently by classical systems. Several fundamental questions arise: Experimentalist's aspect: the next generation of quantum computers will presumably contain a few tens of qubits or more. Such systems are already impossible to simulate efficiently classically. Which experiments should be conducted in order to verify that those claimed quantum computers are performing the way they should? Cryptographic aspect: assuming that the first generations of quantum computers will be extremely expensive, and thus quantum computations would be delegated to untrusted companies. How can one trust the outcome? Moreover, can the tasks being delegated be kept secret? Foundations of Quantum Mechanics aspect: assuming that small systems obey quantum mechanics to an extremely high accuracy, it is still possible that the physical description of large many-body systems deviates significantly from quantum mechanics. The conjecture that BQP is not equal to B...
Cartoon Computation: Quantum-like computing without quantum mechanics
Aerts, Diederik; Czachor, Marek
2006-01-01
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...
Pulse controlled noise suppressed quantum computation
Duan, Lu-ming; Guo, Guang-Can
1998-01-01
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.
Addition on a Quantum Computer
Draper, Thomas G
2000-01-01
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register. This method also allows for massive parallelization in its execution.
Quantum computing for pattern classification
Schuld, Maria; Sinayskiy, Ilya; Petruccione, Francesco
2014-01-01
It is well known that for certain tasks, quantum computing outperforms classical computing. A growing number of contributions try to use this advantage in order to improve or extend classical machine learning algorithms by methods of quantum information theory. This paper gives a brief introduction into quantum machine learning using the example of pattern classification. We introduce a quantum pattern classification algorithm that draws on Trugenberger's proposal for measuring the Hamming di...
International Nuclear Information System (INIS)
It is shown that pure NQR can be utilized as a platform for quantum computing without applying a high external magnetic field. By exciting each resonance transition between quadrupole energy levels with two radio-frequency fields differing in phase and direction, the double degeneracy of the spin energy spectrum in an electric field gradient is removed. As an example, in the case of I=7/2 (nuclei 133Cs or 123Sb) the energy spectrum has eight levels which can be used as three qubits. (orig.)
The universe as quantum computer
Lloyd, Seth
2013-01-01
This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so, just what kind of computer it is. I will show that the universe can be regarded as a giant quantum computer. The quantum computational model of the universe explains a variety of observed phenomena not encompassed by the ordinary laws of physics. In particular, the model shows that the the quantum computational universe automatically gives rise to a mix of randomness and order, and to both simple and complex systems.
THE APROACH OF CLASSICAL COMPUTER TO QUANTUM COMPUTER
Directory of Open Access Journals (Sweden)
SEYEDEH MOHADESEH ELTEJA
2013-09-01
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.
THE APROACH OF CLASSICAL COMPUTER TO QUANTUM COMPUTER
SEYEDEH MOHADESEH ELTEJA
2013-01-01
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.
Quantum Walks, Quantum Gates and Quantum Computers
Hines, Andrew P.; Stamp, P. C. E.
2007-01-01
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 a single- and multi-excitation coding, and for more general mappings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are...
Cluster-state quantum computation
Nielsen, M A
2005-01-01
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster state cannot occur as the exact ground state of any naturally occurring physical system, and a proof that measurements on any quantum state which is linearly prepared in one dimension can be efficiently simulated on a classical computer, and thus are not candidates for use as a substrate for quantum computation.
Experimental Aspects of Quantum Computing
Everitt, Henry O
2005-01-01
Practical quantum computing still seems more than a decade away, and researchers have not even identified what the best physical implementation of a quantum bit will be. There is a real need in the scientific literature for a dialog on the topic of lessons learned and looming roadblocks. These papers, which appeared in the journal of "Quantum Information Processing" are dedicated to the experimental aspects of quantum computing These papers highlight the lessons learned over the last ten years, outline the challenges over the next ten years, and discuss the most promising physical implementations of quantum computing.
Decoherence in quantum walks and quantum computers
Hines, Andrew P.; Stamp, P. C. E.
2007-01-01
Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of system-environment interaction. Whether such methods will be reliable in the face of more realistic models is a fundamental open question. In this partly pedagogical article, we study two toy models of quantum information processing, using the language of \\emph{quantum wa...
Quantum Computing and Dynamical Quantum Models
Aaronson, Scott
2002-01-01
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum state. We study what can be computed by sampling from that distribution, i.e., by examining an observer's entire history. We show that, relative to an oracle, one can solve problems in polynomial time that are intractable even for quantum ...
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.
Universal quantum computation by discontinuous quantum walk
Underwood, Michael S
2010-01-01
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 timestep apart.
Vianna, Reinaldo O.; Rabelo, Wilson R. M.; Monken, C. H.
2003-01-01
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure classical architecture, no matter how few qubits are available and, therefore, it suggests an easier implementable technology than a pure quantum computer with arbitrary number of qubits.
Database Manipulation on Quantum Computers
Younes, Ahmed
2007-01-01
Manipulating a database system on a quantum computer is an essential aim to benefit from the promising speed-up of quantum computers over classical computers in areas that take a vast amount of storage and processing time such as in databases. In this paper, the basic operations for manipulating the data in a quantum database will be defined, e.g. INSERT, UPDATE, DELETE, SELECT, backing up and restoring a database file. This gives the ability to perform the data processing t...
Superconducting Quantum Computing Without Entanglement?
Kadin, Alan M.; Kaplan, Steven B.
2014-01-01
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...
Are Quantum Computing Models Realistic?
Kak, Subhash
2001-01-01
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 uncertainty. We revie...
Quantum computers, factoring, and decoherence
Chuang, I; Shor, P W; Zurek, W H; Chuang, I; Laflamme, Raymond; Shor, P; Zurek, W
1995-01-01
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential (\\sim \\exp L^{1/3}, for a number with L digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in L (\\sim L^2). This enormous speed-up is possible in principle because quantum computation can simultaneously follow all of the paths corresponding to the distinct classical inputs, obtaining the solution as a result of coherent quantum interference between the alternatives. Hence, a quantum computer is sophisticated interference device, and it is essential for its quantum state to remain coherent in the course of the operation. In this report we investigate the effect of decoherence on the quantum...
Visualizing a silicon quantum computer
International Nuclear Information System (INIS)
Quantum computation is a fast-growing, multi-disciplinary research field. The purpose of a quantum computer is to execute quantum algorithms that efficiently solve computational problems intractable within the existing paradigm of 'classical' computing built on bits and Boolean gates. While collaboration between computer scientists, physicists, chemists, engineers, mathematicians and others is essential to the project's success, traditional disciplinary boundaries can hinder progress and make communicating the aims of quantum computing and future technologies difficult. We have developed a four minute animation as a tool for representing, understanding and communicating a silicon-based solid-state quantum computer to a variety of audiences, either as a stand-alone animation to be used by expert presenters or embedded into a longer movie as short animated sequences. The paper includes a generally applicable recipe for successful scientific animation production.
Algorithms on Ensemble Quantum Computers
Boykin, P. Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh
1999-01-01
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements u...
Energy Technology Data Exchange (ETDEWEB)
Koenneker, Carsten (comp.)
2012-11-01
The following topics are dealt with: Reality in the test facility, quantum teleportation, the reality of quanta, interaction-free quantum measurement, rules for quantum computers, quantum computers with ions, spintronics with diamond, the limits of the quantum computers, a view in the future of quantum optics. (HSI)
Quantum physics, simulation, and computation
International Nuclear Information System (INIS)
Full text: The ultimate scope and power of computers will be determined by the laws of physics. Quantum computers exploit the rules of quantum mechanics, using quantum coherence and entanglement for new ways of information processing. Up to date, the realization of these systems requires extremely precise control of matter on the atomic scale and a nearly perfect isolation from the environment. The question, to what extent quantum information processing can also be exploited in 'natural' and less controlled systems, including biological ones, is exciting but still open. In this talk, I will present some of our recent work on (quantum) physically and biologically motivated models of information processing. (author)
Algorithms on ensemble quantum computers.
Boykin, P Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh
2010-06-01
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and ?(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement. PMID:21475662
Simulating chemistry using quantum computers.
Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán
2011-01-01
The difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors. PMID:21166541
Quantum Computing over Finite Fields
James, Roshan P; Sabry, Amr
2011-01-01
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a finite field instead of the field of complex numbers. This instantiation collapses much the structure of actual quantum mechanics but retains several of its distinguishing characteristics including the notions of superposition, interference, and entanglement. Furthermore, discrete quantum theory excludes local hidden variable models, has a no-cloning theorem, and can express natural counterparts of quantum information protocols such as superdense coding and teleportation. Our first result is to distill a model of discrete quantum computing from this quantum theory. The model is expressed using a monadic metalanguage built on top of a universal reversible language for finite computations, and hence is directly implementab...
Silicon-based Quantum Computation
S. Simmons
2013-01-01
There is a worldwide race to build a computer which exploits the counterintuitive principles of quantum mechanics1. Silicon is one of the most promising platforms for emerging quantum information technologies for two reasons: one, it possesses many of the key desirable criteria for low-error quantum information processing, and two, the microelectronics industry has decades of experience with producing ultrapure silicon and nanoscale silicon devices, which makes silicon-based quantum devices a...
Genetic Algorithms and Quantum Computation
Giraldi, G A; Thess, R N; Giraldi, Gilson A.; Portugal, Renato; Thess, Ricardo N.
2004-01-01
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so called Quantum Evolutionary Programming has two major sub-areas: Quantum Inspired Genetic Algorithms (QIGAs) and Quantum Genetic Algorithms (QGAs). The former adopts qubit chromosomes as representations and employs quantum gates for the search of the best solution. The later tries to solve a key question in this field: what GAs will look like as an implementation on quantum hardware? As we shall see, there is not a complete answer for this question. An important point for QGAs is to build a quantum algorithm that takes advantage of both the GA and quantum computing parallelism as well as true randomness provided by quantum computers. In the first part of this paper we present a survey of the main works in GAs plus quantum computing including also our works in this area. He...
Experimental implementations of quantum computers
DiVincenzo, David
2006-01-01
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 communication, quantum computers and ...
The Physics of Quantum Computation
Falci, Giuseppe; Paladino, Elisabette
2015-10-01
Quantum Computation has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. QC has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. In these lecture notes we focus on physical hardware, present day challenges and future directions for design of quantum architectures.
Quantum Computer Using Coupled Quantum Dot Molecules
Wu, N J; Natori, A; Yasunaga, H; Wu*, Nan-Jian
1999-01-01
We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can...
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
Biamonte, Jacob D.; Perkowski, Marek A.
2004-01-01
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.
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)
Cartoon computation: quantum-like computing without quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Aerts, Diederik [Centrum Leo Apostel (CLEA) and Foundations of the Exact Sciences (FUND), Vrije Universiteit Brussel, 1050 Brussels (Belgium); Czachor, Marek [Katedra Fizyki Teoretycznej i Informatyki Kwantowej, Politechnika Gdanska, 80-952 Gdansk (Poland)
2007-03-30
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)
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
Arvind
2001-02-01
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically
Programming Pulse Driven Quantum Computers
Lloyd, Seth
1999-01-01
Arrays of weakly-coupled quantum systems can be made to compute by subjecting them to a sequence of electromagnetic pulses of well-defined frequency and length. Such pulsed arrays are true quantum computers: bits can be placed in superpositions of 0 and 1, logical operations take place coherently, and dissipation is required only for error correction. Programming such computers is accomplished by selecting the proper sequence of pulses.
Focus on topological quantum computation
International Nuclear Information System (INIS)
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This ‘focus on’ collection brings together several of the latest developments in the field and facilitates the synergy between different approaches. (editorial)
Polynomial Simulations of Decohered Quantum Computers
Aharonov, Dorit; Ben-Or, Michael
1996-01-01
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers, or quantum Turing machines(QTM), and (2) parallel quantum computers, or quantum circuits. This paper shows that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. The expected slowdown of...
Quantum measurements with a quantum computer
D'Helon, C
1997-01-01
We present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. The electronic states of the ion become the `apparatus', and the method is based on regarding the `apparatus' as a quantum computer register which can be prepared in appropriate states by running a Fourier transform algorithm on the data stored within it. The resolution of the measurement rises exponentially with the number of ions used.
Quantum Computation Beyond the Circuit Model
Jordan, Stephen P.
2008-01-01
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a ge...
Geometrical perspective on quantum states and quantum computation
Chen, Zeqian
2013-01-01
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 quantum computing a...
Cryptography, quantum computation and trapped ions
Energy Technology Data Exchange (ETDEWEB)
Hughes, Richard J.
1998-03-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
Quantum information and computing
Ohya, M; Watanabe, N
2006-01-01
The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of ?-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum
Surfing Electrons in Quantum Computers?
Pomeau, Y.
I take this opportunity of writing a piece of science for my friend Manuel G. Velarde to discuss things dear to his heart: surfing of electrons on acoustic waves. It has been claimed recently, but not by him, that transport of electrons by surf could be used to carry quantum information in quantum computers. This is physically impossible because this would require to maintain the quantum coherence linked to localisation, a coherence decaying very fastly in the real world.
Quantum computers in phase space
Miquel, Cesar; Paz, Juan Pablo; Saraceno, Marcos
2002-01-01
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 directly measure the Wigner function in a given phas...
Self-correcting quantum computers
Bombin, H.; Chhajlany, R W; Horodecki, M.; Martin-Delgado, M. A.
2013-01-01
Is the notion of a quantum computer (QC) resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting QCs. To this end, we first give a sufficient condition on the connectedness of excitations for a stabilizer code model to be a self-correcting quantum memory. We then study the two main examples of topological stabilizer codes in arbitrary dimensions and establish their self-correcting ca...
Cluster-state quantum computation
Nielsen, Michael A.
2005-01-01
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster state cannot occur as the exact ground state of any naturally occurring physical system, and a proof that measurements on...
Duality quantum computer and the efficient quantum simulations
Wei, Shi-Jie; Long, Gui-Lu
2015-01-01
In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer ...
Blind topological measurement-based quantum computation
Morimae, Tomoyuki; Fujii, Keisuke
2012-01-01
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum 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. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantu...
An Algebra of Reversible Quantum Computing
WANG, Yong
2015-01-01
Based on the axiomatization of reversible computing RACP, we generalize it to quantum reversible computing which is called qRACP. By use of the framework of quantum configuration, we show that structural reversibility and quantum state reversibility must be satisfied simultaneously in quantum reversible computation. RACP and qRACP has the same axiomatization modulo the so-called quantum forward-reverse bisimularity, that is, classical reversible computing and quantum reversible computing are ...
The quantum field as a quantum computer
D'Ariano, Giacomo Mauro
2012-01-01
It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/?, a and ? being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=?c and ?=?(m) mass-dependent. For c the speed of light ? is a vacuum refraction index that increases monotonically from ?(0)=1 to ?(M)=?, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed.
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)
Minimal ancilla mediated quantum computation
Energy Technology Data Exchange (ETDEWEB)
Proctor, Timothy J. [University of Leeds, School of Physics and Astronomy, Leeds (United Kingdom); Kendon, Viv [University of Leeds, School of Physics and Astronomy, Leeds (United Kingdom); Durham University, Department of Physics, Durham (United Kingdom)
2014-12-01
Schemes of universal quantum computation in which the interactions between the computational elements, in a computational register, are mediated by some ancillary system are of interest due to their relevance to the physical implementation of a quantum computer. Furthermore, reducing the level of control required over both the ancillary and register systems has the potential to simplify any experimental implementation. In this paper we consider how to minimise the control needed to implement universal quantum computation in an ancilla-mediated fashion. Considering computational schemes which require no measurements and hence evolve by unitary dynamics for the global system, we show that when employing an ancilla qubit there are certain fixed-time ancilla-register interactions which, along with ancilla initialisation in the computational basis, are universal for quantum computation with no additional control of either the ancilla or the register. We develop two distinct models based on locally inequivalent interactions and we then discuss the relationship between these unitary models and the measurement-based ancilla-mediated models known as ancilla-driven quantum computation. (orig.)
Silicon-based Quantum Computation
Kane, B E
2000-01-01
An architecture for a quantum computer is presented in which spins associatedwith donors in silicon function as qubits. Quantum operations on the spins areperformed using a combination of voltages applied to gates adjacent to thespins and radio frequency applied magnetic fields resonant with spintransitions. Initialization and measurement of electron spins is made byelectrostatic probing of a two electron system, whose orbital configurationmust depend on the spin states of the electrons because of the Pauli Principle.Specific devices will be discussed which perform all the necessary operationsfor quantum computing, with an emphasis placed on the qualitative principlesunderlying their operation. The likely impediments to achieving large-scale quantum computation usingthis architecture will be addressed: the computer must operate at extremely lowtemperature, must be fabricated from devices built with near atomic precision,and will require extremely accurate gating operations in order to performquantum logic. Re...
Quantum chromodynamics with advanced computing
Energy Technology Data Exchange (ETDEWEB)
Kronfeld, Andreas S.; /Fermilab
2008-07-01
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.
Interactive Proofs For Quantum Computations
Aharonov, Dorit; Ben-Or, Michael; Eban, Elad
2008-01-01
The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems perform as they should, if we cannot efficiently compute predictions for their behavior? Vazirani has asked: If predicting Quantum Mechanical systems requires exponential resources, is QM a falsifiable theory? In cryptographic settings, an untrusted future c...
Quantum Computers, Factoring, and Decoherence
Chuang, I.; Laflamme, Raymond; Shor, P.; Zurek, W.
1995-01-01
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\\sim \\exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives fac...
Quantum Computing with Very Noisy Devices
Knill, E.
2004-01-01
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 give evidence that...
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
Physical Realizations of Quantum Computing
Kanemitsu, Shigeru; Salomaa, Martti; Takagi, Shin; Are the DiVincenzo Criteria Fulfilled in 2004 ?
2006-01-01
The contributors of this volume are working at the forefront of various realizations of quantum computers. They survey the recent developments in each realization, in the context of the DiVincenzo criteria, including nuclear magnetic resonance, Josephson junctions, quantum dots, and trapped ions. There are also some theoretical contributions which have relevance in the physical realizations of a quantum computer. This book fills the gap between elementary introductions to the subject and highly specialized research papers to allow beginning graduate students to understand the cutting-edge of r
The quantum field as a quantum computer
Energy Technology Data Exchange (ETDEWEB)
D' Ariano, Giacomo Mauro, E-mail: dariano@unipv.it [University of Pavia, QUIT Group, Dipartimento di Fisica “A. Volta”, via Bassi 6, 27100 Pavia, PV (Italy); Istituto Nazionale di Fisica Nucleare, Gruppo IV, Sezione di Pavia, PV (Italy)
2012-01-16
It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/?, a and ? being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=?c and ?=?(m) mass-dependent. For c the speed of light ?{sup ?1} is a vacuum refraction index that increases monotonically from ?{sup ?1}(0)=1 to ?{sup ?1}(M)=?, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed. -- Highlights: ? q-Computational approach to quantum field theory, the Wheeler's “It from Bit”. ? Dirac derived as free flow of information, without requiring Lorentz covariance. ? Info-interpretation of inertial mass and h{sup ¯} and field Hamiltonian derived from gates. ? Violation of dispersion relation as mass-dependent vacuum refraction index. ? Fermi anticommuting fields substituted by qubits.
Quantum Computing via The Bethe Ansatz
Zhang, Yong
2011-01-01
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a para...
Warp-Drive Quantum Computation
Nakahara, M; Kondo, Y; Tanimura, S; Hata, K; Nakahara, Mikio; Vartiainen, Juha J.; Kondo, Yasushi; Tanimura, Shogo; Hata, Kazuya
2004-01-01
Recently it has been shown that time-optimal quantum computation is attained by using the Cartan decomposition of a unitary matrix. We extend this approach by noting that the unitary group is compact. This allows us to reduce the execution time of a quantum algorithm $U_{\\rm alg}$ further by adding an extra gate $W$ to it. This gate $W$ sends $U_{\\rm alg}$ to another algorithm $WU_{\\rm alg}$ which is executable in a shorter time than $U_{\\rm alg}$. We call this technique warp-drive. Here we show both theoretically and experimentally that the execution time of Grover's algorithm is reduced in two-qubit NMR quantum computer. Warp-drive is potentially a powerful tool in accelerating algorithms and reducing the errors in any realization. of a quantum computer
Faster Quantum Chemistry Simulation on Fault-Tolerant Quantum Computers
Jones, N. Cody; Whitfield, James D; McMahon, Peter L.; Yung, Man-Hong; Van Meter, Rodney; Aspuru-Guzik, Alan; Yamamoto, Yoshihisa
2012-01-01
Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource...
Prospective Algorithms for Quantum Evolutionary Computation
Sofge, Donald A.
2008-01-01
This effort examines the intersection of the emerging field of quantum computing and the more established field of evolutionary computation. The goal is to understand what benefits quantum computing might offer to computational intelligence and how computational intelligence paradigms might be implemented as quantum programs to be run on a future quantum computer. We critically examine proposed algorithms and methods for implementing computational intelligence paradigms, primarily focused on ...
Quantumness, Randomness and Computability
Solis, Aldo; Hirsch, Jorge G.
2015-06-01
Randomness plays a central role in the quantum mechanical description of our interactions. We review the relationship between the violation of Bell inequalities, non signaling and randomness. We discuss the challenge in defining a random string, and show that algorithmic information theory provides a necessary condition for randomness using Borel normality. We close with a view on incomputablity and its implications in physics.
Handbook of computational quantum chemistry
Cook, David B
2005-01-01
Quantum chemistry forms the basis of molecular modeling, a tool widely used to obtain important chemical information and visual images of molecular systems. Recent advances in computing have resulted in considerable developments in molecular modeling, and these developments have led to significant achievements in the design and synthesis of drugs and catalysts. This comprehensive text provides upper-level undergraduates and graduate students with an introduction to the implementation of quantum ideas in molecular modeling, exploring practical applications alongside theoretical explanations.Wri
Maintaining coherence in Quantum Computers
Unruh, W G
1994-01-01
The effect of the inevitable coupling to external degrees of freedom of a quantum computer are examined. It is found that for quantum calculations (in which the maintenance of coherence over a large number of states is important), not only must the coupling be small but the time taken in the quantum calculation must be less than the thermal time scale, $\\hbar/k_B T$. For longer times the condition on the strength of the coupling to the external world becomes much more stringent.
Quantum Computation of Jones' Polynomials
Subramanian, V
2002-01-01
It is one of the challenging problems to construct an efficient quantum algorithm which can compute the Jones' polynomial for any knot or link obtained from closure or capping of a $n$-strand braid. We recapitulate the construction of braid-group ${\\cal B}_n$ representations from vertex models. We perform orthogonal transformation involving quantum Clebsch-Gordan coefficient matrix on the qubit basis to obtain eigen basis for the braiding generators. Using the transformed bases, we propose a quantum algorithm to determine the Jones' Polynomial for any knot or link.
On the Problem of Programming Quantum Computers
de Raedt, Hans; Hams, Anthony; Michielsen, Kristel; Miyashita, Seiji; Saito, Keiji
2000-01-01
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyse the difficulties that are encountered in programming physical implementations of quantum computers. We discuss the origin of the instabilities of quantum algorithms and explore physical mechanisms to enlarge the region(s) of stable operation.
Some foundational aspects of quantum computers and quantum robots.
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.; Physics
1998-01-01
This paper addresses foundational issues related to quantum computing. The need for a universally valid theory such as quantum mechanics to describe to some extent its own validation is noted. This includes quantum mechanical descriptions of systems that do theoretical calculations (i.e. quantum computers) and systems that perform experiments. Quantum robots interacting with an environment are a small first step in this direction. Quantum robots are described here as mobile quantum systems with on-board quantum computers that interact with environments. Included are discussions on the carrying out of tasks and the division of tasks into computation and action phases. Specific models based on quantum Turing machines are described. Differences and similarities between quantum robots plus environments and quantum computers are discussed.
Reversible computing fundamentals, quantum computing, and applications
De Vos, Alexis
2010-01-01
Written by one of the few top internationally recognized experts in the field, this book concentrates on those topics that will remain fundamental, such as low power computing, reversible programming languages, and applications in thermodynamics. It describes reversible computing from various points of view: Boolean algebra, group theory, logic circuits, low-power electronics, communication, software, quantum computing. It is this multidisciplinary approach that makes it unique.Backed by numerous examples, this is useful for all levels of the scientific and academic community, from undergr
Theoretical issues in spin-based quantum dot quantum computation
Hu, Xuedong; Sarma, S. Das
2001-01-01
We review our recent work addressing various theoretical issues in spin-based quantum dot quantum computation and quantum information processing. In particular, we summarize our calculation of electron exchange interaction in two-electron double quantum dots and multi-electron double dots, and discuss the physical implication of our results. We also discuss possible errors and how they can be corrected in spin-based quantum dot quantum computation. We critically assess the c...
Quantum Computation--The Ultimate Frontier
Adami, Chris; Dowling, Jonathan P
2002-01-01
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many different quantum systems are being explored for their suitability to serve as a physical substrate for the quantum computer of the future. I discuss some of the theoretical foundations of quantum computer science, including algorithms and err...
A Short Survey on Quantum Computers
Energy Technology Data Exchange (ETDEWEB)
Kanamori, Yoshito [University of Alabama, Huntsville; Yoo, Seong-Moo [University of Alabama, Huntsville; Pan, W. D. [University of Alabama, Huntsville; Sheldon, Frederick T [ORNL
2006-01-01
Quantum computing is an emerging technology. The clock frequency of current computer processor systems may reach about 40 GHz within the next 10 years. By then, one atom may represent one bit. Electrons under such conditions are no longer described by classical physics and a new model of the computer may be necessary by then. The quantum computer is one proposal that may have merit in dealing with the problems associated with the fact that certain important computationally intense problems present that current (classical) computers cannot solve because they require too much processing time. For example, Shor's algorithm performs factoring a large integer in polynomial time while classical factoring algorithms can do it in exponential time. In this paper we briefly survey the current status of quantum computers, quantum computer systems, and quantum simulators. Keywords Classical computers, quantum computers, quantum computer systems, quantum simulators, Shor's algorithm.
Can quantum chemistry be performed on a small quantum computer?
Wecker, Dave; Clark, Bryan K; Hastings, Matthew B; Troyer, Matthias
2013-01-01
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, ...
Quantum Walks for Computer Scientists
Venegas-Andraca, Salvador
2008-01-01
Quantum computation, one of the latest joint ventures between physics and the theory of computation, is a scientific field whose main goals include the development of hardware and algorithms based on the quantum mechanical properties of those physical systems used to implement such algorithms. Solving difficult tasks (for example, the Satisfiability Problem and other NP-complete problems) requires the development of sophisticated algorithms, many of which employ stochastic processes as their mathematical basis. Discrete random walks are a popular choice among those stochastic processes. Inspir
Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers
Benioff, Paul
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$ is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem w...
Using a quantum computer to investigate quantum chaos
Schack, Ruediger
1997-01-01
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Miao, Xijia
2011-01-01
It is shown in the paper that the unitary quantum dynamics in quantum mechanics 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. On the other hand, the symmetric structure of Hilbert space of a composite quantum system is the quantum-computing resource that is not owned by classical computation. A new quantum-computing speedup theory is se...
Geometric phases and quantum computation
International Nuclear Information System (INIS)
Full text: In my lectures I will talk about the notion of the geometric phase and explain its relevance for both fundamental quantum mechanics as well as quantum computation. The phase will be at first introduced via the idea of Pancharatnam which involves interference of three or more light beams. This notion will then be generalized to the evolving quantum systems. I will discuss both pure and mixed states as well as unitary and non-unitary evolutions. I will also show how the concept of the vacuum induced geometric phase arises in quantum optics. A simple measurement scheme involving a Mach Zehnder interferometer will be presented and will be used to illustrate all the concepts in the lecture. Finally, I will expose a simple generalization of the geometric phase to evolving degenerate states. This will be seen to lead to the possibility of universal quantum computation using geometric effects only. Moreover, this contains a promise of intrinsically fault tolerant quantum information processing, whose prospects will be outlined at the end of the lecture. (author)
Quantum ballistic evolution in quantum mechanics: Application to quantum computers
International Nuclear Information System (INIS)
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proven that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics. Also the definition of quantum Turing machines used here is compared with that used by other authors. copyright 1996 The American Physical Society
Efficient quantum computing insensitive to phase errors
Georgeot, B.; Shepelyansky, D. L.
2001-01-01
We show that certain computational algorithms can be simulated on a quantum computer with exponential efficiency and be insensitive to phase errors. Our explicit algorithm simulates accurately the classical chaotic dynamics for exponentially many orbits even when the quantum fidelity drops to zero. Such phase-insensitive algorithms open new possibilities for computation on realistic quantum computers.
Quantum computing of quantum chaos and imperfection effects
Song, Pil Hun; Shepelyansky, Dima L.
2000-01-01
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.
Self-correcting quantum computers
Bombin, H.; Chhajlany, R. W.; Horodecki, M.; Martin-Delgado, M. A.
2013-05-01
Is the notion of a quantum computer (QC) resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting QCs. To this end, we first give a sufficient condition on the connectedness of excitations for a stabilizer code model to be a self-correcting quantum memory. We then study the two main examples of topological stabilizer codes in arbitrary dimensions and establish their self-correcting capabilities. Also, we address the transversality properties of topological color codes, showing that six-dimensional color codes provide a self-correcting model that allows the transversal and local implementation of a universal set of operations in seven spatial dimensions. Finally, we give a procedure for initializing such quantum memories at finite temperature.
Interaction-free quantum computation
Azuma, H
2004-01-01
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.
Quantum Computation by Geometrical Means
Pachos, Jiannis
2000-01-01
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we present an explicit construction of a universal set of gates, represented by holonomies acting on degenerate states.
Distributed quantum computing: A distributed Shor algorithm
Yimsiriwattana, Anocha; Lomonaco Jr, Samuel J.
2004-01-01
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with po...
ASCR Workshop on Quantum Computing for Science
Energy Technology Data Exchange (ETDEWEB)
Aspuru-Guzik, Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Van Dam, Wim [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Farhi, Edward [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Gaitan, Frank [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Humble, Travis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jordan, Stephen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Landahl, Andrew J [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Love, Peter [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lucas, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Preskill, John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Muller, Richard P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Svore, Krysta [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wiebe, Nathan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Williams, Carl [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-06-01
This report details the findings of the DOE ASCR Workshop on Quantum Computing for Science that was organized to assess the viability of quantum computing technologies to meet the computational requirements of the DOEâ€™s science and energy mission, and to identify the potential impact of quantum technologies. The workshop was held on February 17-18, 2015, in Bethesda, MD, to solicit input from members of the quantum computing community. The workshop considered models of quantum computation and programming environments, physical science applications relevant to DOE's science mission as well as quantum simulation, and applied mathematics topics including potential quantum algorithms for linear algebra, graph theory, and machine learning. This report summarizes these perspectives into an outlook on the opportunities for quantum computing to impact problems relevant to the DOEâ€™s mission as well as the additional research required to bring quantum computing to the point where it can have such impact.
Fault tolerance for holonomic quantum computation
Oreshkov, Ognyan; Brun, Todd A.; Lidar, Daniel A.
2013-01-01
Comment: 16 pages, this is a chapter in the book "Quantum Error Correction", edited by Daniel A. Lidar and Todd A. Brun, (Cambridge University Press, 2013), at http://www.cambridge.org/us/academic/subjects/physics/quantum-physics-quantum-information-and-quantum-computation/quantum-error-correction
Simulating quantum dynamics on a quantum computer
International Nuclear Information System (INIS)
We explicitly show how to simulate time-dependent sparse Hamiltonian evolution on a quantum computer, with complexity that is close to linear in the evolution time. The complexity also depends on the magnitude of the derivatives of the Hamiltonian. We propose a range of techniques to simulate Hamiltonians with badly behaved derivatives. These include using adaptive time steps, adapting the order of the integrators, and omitting regions about discontinuities. The complexity of the algorithm is quantified by calls to an oracle, which yields information about the Hamiltonian, and accounts for all computational resources. We explicitly determine the number of bits of output that this oracle needs to provide, and show how to efficiently perform the required 1-sparse unitary operations using these bits. We also account for discretization error in the time, as well as accounting for Hamiltonians that are a sum of terms that are sparse in different bases. (paper)
The Quantum Way of Doing Computations
International Nuclear Information System (INIS)
Full text: Since the mid nineties of the 20th century it became apparent that one of the centuries’ most important technological inventions, computers in general and many of their applications could possibly be further enormously enhanced by using operations based on quantum. This is timely since the classical road maps for the development of computational devices, commonly known as Moore’s law, will cease to be applicable within the next decade due to the ever smaller sizes of the electronic components that soon will enter the quantum physics realm. Computations, whether they happen in our heads or with any computational device, always rely on real physical processes, which are data input, data representation in a memory, data manipulation using algorithms and finally, the data output. Building a quantum computer then requires the implementation of quantum bits (qubits) as storage sites for quantum information, quantum registers and quantum gates for data handling and processing and the development of quantum algorithms. In this talk, the basic functional principle of a quantum computer will be reviewed and a few technologies for their implementation will be highlighted. In particular, the quantum way of doing computations will be illustrated by showing how quantum correlations, commonly known as entanglement can enhance computational processes. Aside from their use for quantum computers, these quantum technologies open wide perspectives for applications in many technical areas. Examples such as quantum enhanced metrology and quantum simulations will be presented. (author)
Classical computing, quantum computing, and Shor's factoring algorithm
Manin, Yuri I.
1999-01-01
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the P/NP problem are reviewed. Section 2 introduces the notion of quantum parallelism and explains the main issues of quantum computing. Section 3 is devoted to four quantum subroutines: initialization, quantum computing of classical Boolean functions, quantum Fou...
A Quantum to Classical Phase Transition in Noisy Quantum Computers
Aharonov, Dorit
1999-01-01
The fundamental problem of the transition from quantum to classical physics is usually explained by decoherence, and viewed as a gradual process. The study of entanglement, or quantum correlations, in noisy quantum computers implies that in some cases the transition from quantum to classical is actually a phase transition. We define the notion of entanglement length in $d$-dimensional noisy quantum computers, and show that a phase transition in entanglement occurs at a critical noise rate, wh...
Universal quantum computation using the discrete time quantum walk
Lovett, Neil B; Everitt, Matthew; Trevers, Matthew; Kendon, Viv
2009-01-01
A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time quantum walk. We show the discrete time quantum walk is also a computational primitive and is able to implement the same universal gate set. Additionally we give a set of components on which the discrete time quantum walk provides perfect state transfer.
Universal quantum computing with nanowire double quantum dots
Xue, P
2011-01-01
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 emphasize that all techniq...
Computational model underlying the one-way quantum computer
Raussendorf, R; Raussendorf, Robert; Briegel, Hans
2001-01-01
In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett 86, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantum information processing that are possible with the one-way quantum computer can be explained within a network model. As a consequence, the temporal complexity is, for certain algorithms, lower than in networks. For example, every circuit in the Clifford group can be performed on the one-way quantum computer in a single time step.
Classical computing, quantum computing, and Shor's factoring algorithm
Manin, Yu I
1999-01-01
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the P/NP problem are reviewed. Section 2 introduces the notion of quantum parallelism and explains the main issues of quantum computing. Section 3 is devoted to four quantum subroutines: initialization, quantum computing of classical Boolean functions, quantum Fourier transform, and Grover's search algorithm. The central Section 4 explains Shor's factoring algorithm. Section 5 relates Kolmogorov's complexity to the spectral properties of computable function. Appendix contributes to the prehistory of quantum computing.
Warp-Drive Quantum Computation
Nakahara, Mikio; Vartiainen, Juha J.; Kondo, Yasushi; Tanimura, Shogo; Hata, Kazuya
2004-01-01
Recently it has been shown that time-optimal quantum computation is attained by using the Cartan decomposition of a unitary matrix. We extend this approach by noting that the unitary group is compact. This allows us to reduce the execution time of a quantum algorithm $U_{\\rm alg}$ further by adding an extra gate $W$ to it. This gate $W$ sends $U_{\\rm alg}$ to another algorithm $WU_{\\rm alg}$ which is executable in a shorter time than $U_{\\rm alg}$. We call this technique war...
The scalable quantum computation based on quantum dot systems
Zhang, Jian-Qi; Yu, Ya-Fei; Feng, Xun-Li; ZHANG, ZHI-MING
2011-01-01
We propose a scheme for realizing the scalable quantum computation based on nonidentical quantum dots trapped in a single-mode waveguide. In this system, the quantum dots simultaneously interact with a large detuned waveguide and classical light fields. During the process, neither the waveguide mode nor the quantum dots are excited, while the sub-system composed of any two quantum dots can acquire phases conditional upon the states of these two quantum dots and the certain d...
Experimental realization of the quantum games on a quantum computer
Du, J; Xu, X; Shi, M; Wu, J; Zhou, X; Han, R; Du, Jiangfeng; Li, Hui; Xu, Xiaodong; Shi, Mingjun; Wu, Jihui; Zhou, Xianyi; Han, Rongdian
2002-01-01
Many previous works on quantum games are based on maximally entangled state. In this letter, we investigate the role of entanglement in quantum games. For the particular case of the quantum Prisoners' Dilemma, the property of the game changes fascinatingly with the variation of the measure of the game's entanglement. Furthermore this quantum game is experimental realized on our nuclear magnetic resonance quantum computer. Up to now, there is no quantum game in any form become pratical.
Programming physical realizations of quantum computers
de Raedt, Hans; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyze the difficulties that are encountered in programming physical realizations of quantum computers. Examples of logically identical implementations of the controlled-NOT operation and Grover's database search algorithm are used to demonstrate that the results of a quantum computation are unstable with respect to the physical ...
Using Quantum Computers to Learn Physics
Wiebe, Nathan
2014-01-01
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve using existing computers for even modestly large systems. Here I will show that quantum computers can sometimes be used to address such problems and that quantum computer science can assign formal complexities to learning facts about nature. ...
Quantum computing from the ground up
Perry, Riley Tipton
2012-01-01
Quantum computing - the application of quantum mechanics to information - represents a fundamental break from classical information and promises to dramatically increase a computer's power. Many difficult problems, such as the factorization of large numbers, have so far resisted attack by classical computers yet are easily solved with quantum computers. If they become feasible, quantum computers will end standard practices such as RSA encryption. Most of the books or papers on quantum computing require (or assume) prior knowledge of certain areas such as linear algebra or quantum mechanics. The majority of the currently-available literature is hard to understand for the average computer enthusiast or interested layman. This text attempts to teach quantum computing from the ground up in an easily readable way, providing a comprehensive tutorial that includes all the necessary mathematics, computer science and physics.
The Next Generation Computing Brainwave-Quantum Computing
T.Venkat Narayana Rao; Shirish Pathania
2010-01-01
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...
Quantum Computation and Decision Trees
Farhi, E; Farhi, Edward; Gutmann, Sam
1998-01-01
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root. We devise a quantum mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level n in time polynomial in n, then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in n, but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
KLM quantum computation as a measurement based computation
Popescu, Sandu
2006-01-01
We show that the Knill Laflamme Milburn method of quantum computation with linear optics gates can be interpreted as a one-way, measurement based quantum computation of the type introduced by Briegel and Rausendorf. We also show that the permanent state of n n-dimensional systems is a universal state for quantum computation.
Problems and solutions in quantum computing and quantum information
Steeb, Willi-Hans
2012-01-01
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, deportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, number states and Bose operators, coherent states, squeezed states, Gaussian states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton opera...
Exponential Gain in Quantum Computing of Quantum Chaos and Localization
Georgeot, B.; Shepelyansky, D. L.
2000-01-01
We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps.
Quantum computing with parafermions
Hutter, Adrian; Loss, Daniel
2016-03-01
Zd parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case d =2 . In contrast to Majorana fermions, braiding of parafermions with d >2 allows one to perform an entangling gate. This has spurred interest in parafermions, and a variety of condensed matter systems have been proposed as potential hosts for them. In this work, we study the computational power of braiding parafermions more systematically. We make no assumptions on the underlying physical model but derive all our results from the algebraical relations that define parafermions. We find a family of 2 d representations of the braid group that are compatible with these relations. The braiding operators derived this way reproduce those derived previously from physical grounds as special cases. We show that if a d -level qudit is encoded in the fusion space of four parafermions, braiding of these four parafermions allows one to generate the entire single-qudit Clifford group (up to phases), for any d . If d is odd, then we show that in fact the entire many-qudit Clifford group can be generated.
Quantum computation with programmable connections between gates
Energy Technology Data Exchange (ETDEWEB)
Colnaghi, Timoteo, E-mail: timoteo.colnaghi@gmail.com [QUIT group, Dipartimento di Fisica, via Bassi 6, 27100 Pavia (Italy); D' Ariano, Giacomo Mauro [QUIT group, Dipartimento di Fisica, via Bassi 6, 27100 Pavia (Italy); INFN Gruppo IV, Sezione di Pavia, via Bassi, 6, 27100 Pavia (Italy); Facchini, Stefano, E-mail: stefano.facchini@unipv.it [QUIT group, Dipartimento di Fisica, via Bassi 6, 27100 Pavia (Italy); Perinotti, Paolo [QUIT group, Dipartimento di Fisica, via Bassi 6, 27100 Pavia (Italy); INFN Gruppo IV, Sezione di Pavia, via Bassi, 6, 27100 Pavia (Italy)
2012-10-01
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.
Brain Neurons as Quantum Computers:
Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.
The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.
Quantum ballistic evolution in quantum mechanics: Application to quantum computers
Energy Technology Data Exchange (ETDEWEB)
Benioff, P. [Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
1996-08-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators {ital T} is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that {ital T} must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that {ital T} is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proven that, given a step operator {ital T} for an arbitrary {ital deterministic} quantum Turing machine, it is decidable if {ital T} is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if {ital T} is a step operator for a {ital nondeterministic} machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics. Also the definition of quantum Turing machines used here is compared with that used by other authors. {copyright} {ital 1996 The American Physical Society.}
Cove: A Practical Quantum Computer Programming Framework
Purkeypile, Matt
2009-01-01
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.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail. PMID:24005379
Towards Linear Optical Quantum Computers
Dowling, Jonathan P; Franson, James D.; Lee, Hwang; Milburn, Gerald J.
2004-01-01
Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear interaction between the two photons, and the efficiency of this nonlinear interaction is typically very tiny in bulk materials. However, we recently have shown that this barrier can be circumvented with effective nonlinearities produced by projective measurements, ...
Dynamical Imperfections in quantum computers
Facchi, Paolo; Montangero, Simone; Fazio, Rosario; Pascazio, Saverio
2004-01-01
We study the effects of dynamical imperfections in quantum computers. By considering an explicit example, we identify different regimes ranging from the low-frequency case, where the imperfections can be considered as static but with renormalized parameters, to the high frequency fluctuations, where the effects of imperfections are completely wiped out. We generalize our results by proving a theorem on the dynamical evolution of a system in the presence of dynamical perturbations.
Geometry of discrete quantum computing
International Nuclear Information System (INIS)
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 Fp2 (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 CP2n-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 DCP2n-1, the discrete analogue of the complex projective space, which has p2n-1(p-1) ?k=1n-1( p2k+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 Fp2 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. (paper)
EXPLORATIONS IN QUANTUM COMPUTING FOR FINANCIAL APPLICATIONS
Gare, Jesse
2010-01-01
Quantum computers have the potential to increase the solution speed for many computational problems. This paper is a first step into possible applications for quantum computing in the context of computational finance. The fundamental ideas of quantum computing are introduced, followed by an exposition of the algorithms of Deutsch and Grover. Improved mean and median estimation are shown as results of Grover?s generalized framework. The algorithm for mean estimation is refined to an improved M...
A quantum computing primer for operator theorists
Kribs, David W
2004-01-01
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum channels, or equivalently, completely positive trace preserving maps. The main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations. PMID:22652702
Transparallel mind: Classical computing with quantum power
van der Helm, Peter A.
2014-01-01
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 special distributed representations called hyperstrings. Hyperstrings are superpositions of up to an exponential number of st...
RISQ - reduced instruction set quantum computers
Molmer, Klaus; Sorensen, Anders
2000-01-01
Candidates for quantum computing which offer only restricted control, e.g., due to lack of access to individual qubits, are not useful for general purpose quantum computing. We present concrete proposals for the use of systems with such limitations as RISQ - reduced instruction set quantum computers and devices - for simulation of quantum dynamics, for multi-particle entanglement and squeezing of collective spin variables. These tasks are useful in their own right, and they also provide exper...
From Monte Carlo to Quantum Computation
Heinrich, Stefan
2001-01-01
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring over classical deterministic or randomized methods for this type of problem. In this paper we give a short introduction to the basic ideas of quantum computing and survey recent results on high dimensional integration. We discuss connections to the Monte Carl...
Exploiting locality in quantum computation for quantum chemistry
McClean, Jarrod R; Love, Peter J; Aspuru-Guzik, Alán
2014-01-01
Accurate prediction of chemical and material properties from first principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route towards highly accurate solutions with polynomial cost, however this solution still carries a large overhead. In this perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provide numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.
Computational multiqubit tunnelling in programmable quantum annealers
Boixo, Sergio; Smelyanskiy, Vadim N.; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Denchev, Vasil S.; Amin, Mohammad H.; Smirnov, Anatoly Yu; Mohseni, Masoud; Neven, Hartmut
2016-01-01
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.
Computational multiqubit tunnelling in programmable quantum annealers.
Boixo, Sergio; Smelyanskiy, Vadim N; Shabani, Alireza; Isakov, Sergei V; Dykman, Mark; Denchev, Vasil S; Amin, Mohammad H; Smirnov, Anatoly Yu; Mohseni, Masoud; Neven, Hartmut
2016-01-01
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. PMID:26739797
Quantum ballistic evolution in quantum mechanics application to quantum computers
Benioff, P
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also pr...
The Next Generation Computing Brainwave-Quantum Computing
Directory of Open Access Journals (Sweden)
T. Venkat Narayana Rao
2010-12-01
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.
Efficient Simulation of Quantum Systems by Quantum Computers
Zalka, Christof
1996-01-01
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a conventional simulation of the corresponding classical system. We then sketch how results of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum ...
Toward a superconducting quantum computer: Harnessing macroscopic quantum coherence
Tsai, Jaw-Shen
2010-01-01
Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still man...
Suppression of quantum chaos in a quantum computer hardware
International Nuclear Information System (INIS)
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
Suppression of quantum chaos in a quantum computer hardware.
Lages, J; Shepelyansky, D L
2006-08-01
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. PMID:17025526
Quantum computation speedup limits from quantum metrological precision bounds
Demkowicz-Dobrzanski, Rafal; Markiewicz, Marcin
2014-01-01
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and quantum computing schemes becomes clear. More importantly, we utilize results from the field of quantum metrology on a generic loss of quadratic quantum precision enhancement in presence of decoherence to infer an analogous generic loss o...
Geometry of Quantum Computation with Qudits
Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun
2014-01-01
The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound.
The Quantum Human Computer (QHC) Hypothesis
Salmani-Nodoushan, Mohammad Ali
2008-01-01
This article attempts to suggest the existence of a human computer called Quantum Human Computer (QHC) on the basis of an analogy between human beings and computers. To date, there are two types of computers: Binary and Quantum. The former operates on the basis of binary logic where an object is said to exist in either of the two states of 1 and…
Layered Architectures for Quantum Computers and Quantum Repeaters
Jones, Nathan C.
This chapter examines how to organize quantum computers and repeaters using a systematic framework known as layered architecture, where machine control is organized in layers associated with specialized tasks. The framework is flexible and could be used for analysis and comparison of quantum information systems. To demonstrate the design principles in practice, we develop architectures for quantum computers and quantum repeaters based on optically controlled quantum dots, showing how a myriad of technologies must operate synchronously to achieve fault-tolerance. Optical control makes information processing in this system very fast, scalable to large problem sizes, and extendable to quantum communication.
Nanophotonic quantum computer based on atomic quantum transistor
Andrianov, S. N.; Moiseev, S. A.
2015-10-01
We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks.
Quantum Computations and Images Recognition
Vlasov, A Yu
1997-01-01
The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of qubit spaces). For example, for algorithm of factorization of numbers by quantum computer n can be about a few hundreds for some realistic applications for cryptography. The applications described further are used some other properties of quantum systems and they do not demand such huge number of states. The term "images recognition" is used here for some broad class of problems. For example, we have a set of some objects V_i and function of "likelihood": F(V,W) < F(V,V) = 1 If we have some "noisy" or "distorted" image W, we can say that recognition of W is V_i, if F(W,V_i) is near 1 for some V_i.
Composite pulses in NMR quantum computation
Jones, Jonathan A.
2009-01-01
I describe the use of techniques based on composite rotations to combat systematic errors in quantum logic gates. Although developed and described within the context of Nuclear Magnetic Resonance (NMR) quantum computing these sequences should be applicable to other implementations of quantum computation.
Adiabatic quantum computation and quantum annealing theory and practice
McGeoch, Catherine C
2014-01-01
Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov
Quantum machine learning what quantum computing means to data mining
Wittek, Peter
2014-01-01
Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine L
Topological Quantum Computation by Manipulating Toric Code
Kou, Su-Peng
2008-01-01
Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building {fault tolerance} quantum computer by tuning the tunneling of the degenerate quantum states in Z2 topological order, instead of by braiding anyons. Using a designer Hamiltonian - the Wen-Plaquette model as an example, we show how to control the toric code to realize topological quantum computation (TQC). In particular, we give a proposal to the measurement of TQC. In the end the realization of the Wen-Plaquette model in cold atoms is discussed.
The Heisenberg Representation of Quantum Computers
Gottesman, Daniel
1998-01-01
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 importa...
Parallel computing and quantum chromodynamics
Bowler, K C
1999-01-01
The study of Quantum Chromodynamics (QCD) remains one of the most challenging topics in elementary particle physics. The lattice formulation of QCD, in which space-time is treated as a four- dimensional hypercubic grid of points, provides the means for a numerical solution from first principles but makes extreme demands upon computational performance. High Performance Computing (HPC) offers us the tantalising prospect of a verification of QCD through the precise reproduction of the known masses of the strongly interacting particles. It is also leading to the development of a phenomenological tool capable of disentangling strong interaction effects from weak interaction effects in the decays of one kind of quark into another, crucial for determining parameters of the standard model of particle physics. The 1980s saw the first attempts to apply parallel architecture computers to lattice QCD. The SIMD and MIMD machines used in these pioneering efforts were the ICL DAP and the Cosmic Cube, respectively. These wer...
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
Quantum computing with superconductors I: Architectures
Geller, Michael R.; Pritchett, Emily J.; Sornborger, Andrew T.; Wilhelm, F.K.
2006-01-01
Josephson junctions have demonstrated enormous potential as qubits for scalable quantum computing architectures. Here we discuss the current approaches for making multi-qubit circuits and performing quantum information processing with them.
Information and Computation: Classical and Quantum Aspects
Galindo, A; Martin-Delgado, M. A.
2001-01-01
Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportat...
The Essence of Quantum Theory for Computers
Parke, W. C.
2014-01-01
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond those in the familiar classical world. To help in this thinking, we give a description of the foundational ideas that hold in all of our successful physical models, including quantum theory. Our emphasis will be on the proper interpretation of our theories, a...
Quantum Computing and Zeroes of Zeta Functions
van Dam, Wim
2004-01-01
A possible connection between quantum computing and Zeta functions of finite field equations is described. Inspired by the 'spectral approach' to the Riemann conjecture, the assumption is that the zeroes of such Zeta functions correspond to the eigenvalues of finite dimensional unitary operators of natural quantum mechanical systems. The notion of universal, efficient quantum computation is used to model the desired quantum systems. Using eigenvalue estimation, such quantu...
Polynomial simulations of decohered quantum computers
Energy Technology Data Exchange (ETDEWEB)
Aharonov, D.; Ben-Or, M. [Hebrew Univ., Jerusalem (Israel)
1996-12-31
Recently it has become clear, that a key issue in quantum computation is understanding how interaction with the environment, or {open_quote}decoherence{close_quotes}, effects the computational power of quantum computers. We adopt the standard physical method of describing systems which are interwound with their environment by {open_quotes}density matrices{close_quotes}, and within this framework define a model of decoherence in quantum computation. Our results show that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. We first present a simulation of decohered sequential quantum computers, on a classical probabilistic Turing machine, and prove that the expected slowdown of this simulation is polynomial in time and space of the quantum computation, for any non zero decoherence rate. Similar results hold for Quantum computers that are allowed to operate on logarithmic number of qubits at a time. For decohered quantum circuits (with local gates), the situation is more subtle and depends on the decoherence rate, {eta}. We find that our simulation is efficient for circuits with decoherence rate {eta} higher than some constant {eta}{sub 1}, but exponential for a general (random) circuit subjected to decoherence rate lower than some constant {eta}{sub 2}. The transition from exponential cost to polynomial cost happens in a short range of decoherence rates. We use computer experiments to exhibit the phase transitions in various quantum circuits.
The Physical Implementation of Quantum Computation
DiVincenzo, David P.; IBM
2000-01-01
After a brief introduction to the principles and promise of quantum information processing, the requirements for the physical implementation of quantum computation are discussed. These five requirements, plus two relating to the communication of quantum information, are extensively explored and related to the many schemes in atomic physics, quantum optics, nuclear and electron magnetic resonance spectroscopy, superconducting electronics, and quantum-dot physics, for achievin...
Quantum fields on the computer
1992-01-01
This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.
Blind topological measurement-based quantum computation.
Morimae, Tomoyuki; Fujii, Keisuke
2012-01-01
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum 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. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3 × 10(-3), which is comparable to that (7.5 × 10(-3)) of non-blind topological quantum computation. As the error per gate of the order 10(-3) was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach. PMID:22948818
Contextuality supplies the 'magic' for quantum computation.
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-19
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms. PMID:24919152
From Monte Carlo to Quantum Computation
Heinrich, S
2001-01-01
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring over classical deterministic or randomized methods for this type of problem. In this paper we give a short introduction to the basic ideas of quantum computing and survey recent results on high dimensional integration. We discuss connections to the Monte Carlo methology and compare the optimal error rates of quantum algorithms to those of classical deterministic and randomized algorithms.
The Halting Problem for Quantum Computers
Linden, Noah; Popescu, Sandu
1998-01-01
We argue that the halting problem for quantum computers which was first raised by Myers, is by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties that arise in a quantum computer when different branches of the computation halt at different, unknown, times.
Active stabilisation, quantum computation and quantum state synthesis
Steane, A M
1997-01-01
Active stabilisation of a quantum system is the active suppression of noise (such as decoherence) in the system, without disrupting its unitary evolution. Quantum error correction suggests the possibility of achieving this, but only if the recovery network can suppress more noise than it introduces. A general method of constructing such networks is proposed, which gives a substantial improvement over previous fault tolerant designs. The construction permits quantum error correction to be understood as essentially quantum state synthesis. An approximate analysis implies that algorithms involving very many computational steps on a quantum computer can thus be made possible.
A Quantum to Classical Phase Transition in Noisy Quantum Computers
Aharonov, D
1999-01-01
The fundamental problem of the transition from quantum to classical physics is usually explained by decoherence, and viewed as a gradual process. The study of entanglement, or quantum correlations, in noisy quantum computers implies that in some cases the transition from quantum to classical is actually a phase transition. We define the notion of entanglement length in $d$-dimensional noisy quantum computers, and show that a phase transition in entanglement occurs at a critical noise rate, where the entanglement length transforms from infinite to finite. Above the critical noise rate, macroscopic classical behavior is expected, whereas below the critical noise rate, subsystems which are macroscopically distant one from another can be entangled. The macroscopic classical behavior in the super-critical phase is shown to hold not only for quantum computers, but for any quantum system composed of macroscopically many finite state particles, with local interactions and local decoherence, subjected to some addition...
Quantum computation speedup limits from quantum metrological precision bounds
Demkowicz-Dobrza?ski, Rafa?; Markiewicz, Marcin
2015-06-01
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and quantum computing schemes becomes clear. More importantly, we utilize results from the field of quantum metrology on a generic loss of quadratic quantum precision enhancement in the presence of decoherence to infer an analogous generic loss of quadratic speedup in oracle based quantum computing. While most of our reasoning is rigorous, at one of the final steps, we need to make use of an unproven technical conjecture. We hope that we will be able to amend this deficiency in the near future, but we are convinced that even without the conjecture proven our results provide a deep insight into the relationship between quantum algorithms and quantum metrology protocols.
Helping Students Learn Quantum Mechanics for Quantum Computing
Singh, Chandralekha
2016-01-01
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
An introduction to reliable quantum computation
Aliferis, Panos
2011-01-01
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.
Mini-maximizing two qubit quantum computations
Khan, Faisal Shah; Phoenix, Simon J. D.
2013-12-01
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.
The Power of Noisy Fermionic Quantum Computation
de Melo, F.; Cwiklinski, P.; Terhal, B.
2012-01-01
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 [Phys. Rev. A 73, 042313 (2006)] that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular 4-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated cla...
Quantum Computing in Solid State Systems
Ruggiero, B; Granata, C
2006-01-01
The aim of Quantum Computation in Solid State Systems is to report on recent theoretical and experimental results on the macroscopic quantum coherence of mesoscopic systems, as well as on solid state realization of qubits and quantum gates. Particular attention has been given to coherence effects in Josephson devices. Other solid state systems, including quantum dots, optical, ion, and spin devices which exhibit macroscopic quantum coherence are also discussed. Quantum Computation in Solid State Systems discusses experimental implementation of quantum computing and information processing devices, and in particular observations of quantum behavior in several solid state systems. On the theoretical side, the complementary expertise of the contributors provides models of the various structures in connection with the problem of minimizing decoherence.
Disciplines, models, and computers: the path to computational quantum chemistry.
Lenhard, Johannes
2014-12-01
Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990. PMID:25571750
Quantum Computational Logics and Possible Applications
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Leporini, Roberto; di Francia, Giuliano Toraldo
2008-01-01
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).
Difficulties in the Implementation of Quantum Computers
Ponnath, Abhilash
2006-01-01
This paper reviews various engineering hurdles facing the field of quantum computing. Specifically, problems related to decoherence, state preparation, error correction, and implementability of gates are considered.
Quantum-mechanical computers and uncomputability
Energy Technology Data Exchange (ETDEWEB)
Lloyd, S. (Complex Systems Group (T-13) and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States))
1993-08-09
The time evolution operator for any quantum-mechanical computer is diagonalizable, but to obtain the diagonal decomposition of a program state of the computer is as hard as actually performing the computation corresponding to the program. In particular, if a quantum-mechanical system is capable of universal computation, then the diagonal decomposition of program states is uncomputable. As a result, in a universe in which local variables support universal computation, a quantum-mechanical theory for that universe that supplies its spectrum cannot supply the spectral decomposition of the computational variables. A theory of everything'' can be simultaneously correct and fundamentally incomplete.
Computing quantum discord is NP-complete
International Nuclear Information System (INIS)
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. (paper)
The Heisenberg representation of quantum computers
Energy Technology Data Exchange (ETDEWEB)
Gottesman, D.
1998-06-24
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.
The Heisenberg Representation of Quantum Computers
Gottesman, D
1998-01-01
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.
Schrodinger cat animated on a quantum computer
Chepelianskii, A D
2002-01-01
We present a quantum algorithm which allows to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens new possibilities for investigation of macroscopic quantum tunneling and realization of semiclassical Schr\\"odinger cat oscillations. Our numerical studies determine the decoherence rate induced by noisy gates for these oscillations and propose a suitable parameter regime for their experimental implementation.
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Treatment of sound on quantum computers
Lee, Jae Weon; Chepelianskii, Alexei; Shepelyansky, Dima
2003-01-01
We study numerically how a sound signal stored in a quantum computer can be recognized and restored with a minimal number of measurements in presence of random quantum gate errors. A method developed uses elements of MP3 sound compression and allows to recover human speech and sound of complex quantum wavefunctions.
Quantum Computer Games: Schrodinger Cat and Hounds
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements andâ€¦
Communication Links for Distributed Quantum Computation
Van Meter, Rodney; Munro, W J
2007-01-01
Distributed quantum computation requires quantum operations that act over a distance on error-correction encoded states of logical qubits, such as the transfer of qubits via teleportation. We evaluate the performance of several quantum error correction codes, and find that teleportation failure rates of one percent or more are tolerable when two levels of the [[23,1,7
Quantum Teleportation is a Universal Computational Primitive
Gottesman, D; Gottesman, Daniel; Chuang, Isaac L.
1999-01-01
We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.
How to test the ``quantumness'' of a quantum computer?
Zagoskin, Alexandre; Il'ichev, Evgeni; Grajcar, Miroslav; Betouras, Joseph; Nori, Franco
2014-05-01
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.
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-01
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation. PMID:23432228
The one-way quantum computer - a non-network model of quantum computation
Raussendorf, R; Briegel, H J; Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J.
2001-01-01
A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)
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
Quantum state diffusion, localization and computation
Schack, R; Percival, I C
1995-01-01
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage of the localization of quantum states into wave packets occupying small regions of classical phase space. Following and extending the original proposal of Percival, Alber and Steimle, we show that MQSD can provide a further gain over ordinary QSD and other quantum trajectory methods of many orders of magnitude in computational space and time. Because of these gains, it is even possible to calculate an open quantum system trajectory when the corresponding isolated system is intractable. MQSD is particularly advantageous where classical or semiclassical dynamics provides an adequate qualitative picture but is numerically inaccurate because of significant quantum effects. The principles are illustrated by computations for the quantum Duffing oscillator and for second harmonic...
Quantum computing in a piece of glass
Miller, Warner A; Tison, Christopher; Alsing, Paul M; McDonald, Jonathan R
2011-01-01
Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon's linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of quantum computing within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate - the timeless nature of quantum computing. Second, photon entanglement can be encoded as a superposition state of a single photon in a higher-dimensional state space afforded by LM. Our theoretical and numerical results indicate that OptiGrate's photo-thermal refractive (PTR) glass is an enabling technology. We will review our previous design of a quantum projection operator and give credence to this approach on a representative quantum gate grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We disc...
An introduction to measurement based quantum computation
Jozsa, R
2005-01-01
In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel co...
Mathematical Foundations of Holonomic Quantum Computer
Fujii, Kazuyuki
2000-01-01
We make a brief review of (optical) Holonomic Quantum Computer (or Computation) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos and Chountasis (quant-ph/9912093), and give a mathematical reinforcement to their works.
Monte Carlo Simulation of Quantum Computation
Cerf, N J
1998-01-01
The many-body dynamics of a quantum computer can be reduced to the time evolution of non-interacting quantum bits in auxiliary fields by use of the Hubbard-Stratonovich representation of two-bit quantum gates in terms of one-bit gates. This makes it possible to perform the stochastic simulation of a quantum algorithm, based on the Monte Carlo evaluation of an integral of dimension polynomial in the number of quantum bits. As an example, the simulation of the quantum circuit for the Fast Fourier Transform is discussed.
Universality and programmability of quantum computers
Fouche', Willem; Heidema, Johannes; Jones, Glyn; Potgieter, Petrus H.
2007-01-01
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Fey...
Geometry of Quantum Computation with Qudits
Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun
2014-01-01
The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710
Geometry of quantum computation with qudits.
Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun
2014-01-01
The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(d(n)). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710
Quantum Neural Computation for Option Price Modelling
Ivancevic, Vladimir G.
2009-01-01
We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\\"odinger equation, as a result we get a nonlinear Schr\\"odinger equation (NLS), performing as a quantum stochastic filter. In this paper, we present a bidirectional quantum associative memory model for the Black--Scholes--like option price evolution, consisting of a pair of c...
AN INTRODUCTION TO QUANTUM NEURAL COMPUTING
Directory of Open Access Journals (Sweden)
Shaktikanta Nayak
2011-09-01
Full Text Available The goal of the artificial neural network is to create powerful artificial problem solving systems. The field of quantum computation applies ideas from quantum mechanics to the study of computation and has made interesting progress. Quantum Neural Network (QNN is one of the new paradigms built upon the combination of classical neural computation and quantum computation. It is argued that the study of QNN may explain the brain functionality in a better way and create new systems for information processing including solving some classically intractable problems. In this paper we have given an introductory representation of quantum artificial neural network to show how it can be modelled on the basis of double-slit experiment. Also an attempt is made to show the quantum mechanical representation of a classical neuron to implement Hadamard transformation.
Mathematical Aspects of Quantum Computing 2007
Nakahara, Mikio; Rahimi, Robabeh; SaiToh, Akira
2008-04-01
Quantum computing: an overview / M. Nakahara -- Braid group and topological quantum computing / T. Ootsuka, K. Sakuma -- An introduction to entanglement theory / D. J. H. Markham -- Holonomic quantum computing and its optimization / S. Tanimura -- Playing games in quantum mechanical settings: features of quantum games / S. K. Özdemir, J. Shimamura, N. Imoto -- Quantum error-correcting codes / M. Hagiwara -- Poster summaries. Controled teleportation of an arbitrary unknown two-qubit entangled state / V. Ebrahimi, R. Rahimi, M. Nakahara. Notes on the Dür-Cirac classification / Y. Ota, M. Yoshida, I. Ohba. Bang-bang control of entanglement in Spin-Bus-Boson model / R. Rahimi, A. SaiToh, M. Nakahara. Numerical computation of time-dependent multipartite nonclassical correlation / A. SaiToh ... [et al.]. On classical no-cloning theorem under Liouville dynamics and distances / T. Yamano, O. Iguchi.
The potential of the quantum computer
2006-01-01
The Physics Section of the University of Geneva is continuing its series of lectures, open to the general public, on the most recent developments in the field of physics. The next lecture, given by Professor Michel Devoret of Yale University in the United States, will be on the potential of the quantum computer. The quantum computer is, as yet, a hypothetical machine which would operate on the basic principles of quantum mechanics. Compared to standard computers, it represents a significant gain in computing power for certain complex calculations. Quantum operations can simultaneously explore a very large number of possibilities. The correction of quantum errors, which until recently had been deemed impossible, has now become a well-established technique. Several prototypes for, as yet, very simple quantum processors have been developed. The lecture will begin with a demonstration in the auditorium of the detection of cosmic rays and, in collaboration with Professor E. Ellberger of the Conservatoire de M...
Problems and solutions in quantum computing and quantum information
Steeb, Willi-Hans
2004-01-01
Quantum computing and quantum information are two of thefastest-growing and most exciting research areas in physics. Thepossibilities of using non-local behaviour of quantum mechanics tofactorize integers in random polynomial time have added to this newinterest. This invaluable book provides a collection of problems inquantum computing and quantum information together with detailedsolutions. It consists of two parts: in the first partfinite-dimensional systems are considered, while the second part dealswith finite-dimensional systems. All the important concepts and topics are included, such as
Quantum computing with incoherent resources and quantum jumps
Santos, Marcelo F; Chaves, Rafael; Carvalho, Andre R R
2011-01-01
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify by showing how to teleport an unknown quantum state and how to efficiently prepare graph states for the implementation of measurement-based quantum computation.
Quantum computation architecture using optical tweezers
DEFF Research Database (Denmark)
Weitenberg, Christof; Kuhr, Stefan; Mølmer, Klaus; Sherson, Jacob
2011-01-01
We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits...... quantum computing....
Wavelets and Wavelet Packets on Quantum Computers
Klappenecker, Andreas
1999-01-01
We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.
Selecting ensembles for rare earth quantum computation
Sellars, J. J. Longdell M. J.
2003-01-01
We discuss the issues surrounding the implementation of quantum computation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits. Possibilities for a scalable quantum computer are discussed.
Decoherence, Control, and Symmetry in Quantum Computers
Bacon, D
2003-01-01
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on ...
An Axiomatic System Suggested by Quantum Computation
LEPORINI, ROBERTO; BERTINI, CESARINO
2009-01-01
The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information process...
Prospects for Spin-Based Quantum Computing
Kloeffel, Christoph; Loss, Daniel
2012-01-01
Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a remarkable evolution of the field where decoherence, one of the main challenges for realizing quantum computers, no longer seems to be the stumbling block it had originally been considered. General concepts, relevant quantities, and basic re...
Error correction and symmetrization in quantum computers
Peres, Asher
1996-01-01
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the computer, and forcing their joint quantum state to be completely symmetric. On the other hand, isolated errors can be corrected by quantum codewords that represent a logical qubit in a redundant way, by several physical qubits. If one of the physical qubit...
Quantum computation over the butterfly network
Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S.; Murao, Mio
2010-01-01
In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider 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 \\textbf{76}, 040301(R) (2007)], which...
Quantum Computing and the Jones Polynomial
Kauffman, Louis H.
2001-01-01
This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a unitary representation of the braid group. We discuss the evaluation of the polynomial as a generalized quantum amplitude and show how the braiding part of the evaluation can be construed as a quantum computation when the braiding representation is unitary. The q...
The scalable quantum computation based on quantum dot systems
Zhang, Jian-Qi; Feng, Xun-Li; Zhang, Zhi-Ming
2011-01-01
We propose a scheme for realizing the scalable quantum computation based on the system of quantum dots trapped in a single-mode waveguide. In this system, the quantum dots simultaneously interact with a large detuned waveguide and classical light fields. During the process, neither the waveguide mode nor the quantum dots are excited, so the decoherence can be suppressed, while the system can acquire phases conditional upon the states of any two quantum dots. Therefore, it can be used to realize graph states, one qubit controlling multi-qubit phase $\\pi $ gate, and cluster states.
Foundations of Quantum Mechanics and Quantum Computation
Aspect, Alain; Leggett, Anthony; Preskill, John; Durt, Thomas; Pironio, Stefano
2013-03-01
I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantum mechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantum mechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.
Quantum Multiplexing for Quantum Computer Networks
Garcia-Escartin, J C; Chamorro-Posada, Pedro; Garcia-Escartin, Juan Carlos
2007-01-01
In communication networks many different channels must share a limited amount of resources. In order to allow for multiple simultaneous communications, multiple access techniques are routinely employed. With quantum communication, it is possible to share a new kind of resource. All of the system channels can be accommodated into a single channel in a larger Hilbert space. In the scheme, a single line combines the information of all the users, and, at the receiver, the original quantum channels are recovered. The given multiplexer/demultiplexer circuit can perform this n qubits to qudit transformation. Connections with superdense coding and classical multiple access schemes are discussed.
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.
Quantum computer: an appliance for playing market games
Piotrowski, Edward W.; Jan Sladkowski
2003-01-01
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game theory. The paper contain an analysis of such markets that shows that there would be advantage in using quantum computers and quantum strategies.
Quantum Computer Condition: Stability, Classical Computation and Norms
Gilbert, G; Thayer, F J; Weinstein, Yu S; Gilbert, Gerald; Hamrick, Michael; Weinstein, Yaakov S.
2005-01-01
The Quantum Computer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantum computers. In this paper we apply the QCC to the problem of fluctuations and systematic errors in the values of characteristic parameters in realistic systems. We show that fault-tolerant quantum computation is possible despite variations in these parameters. We also use the QCC to explicitly show that reliable classical computation can be carried out using as input the results of fault-tolerant, but imperfect, quantum computation. Finally, we consider the advantages and disadvantages of the superoperator and diamond norms in connection with application of the QCC to various quantum information-theoretic problems.
No quantum advantage for nonlocal computation
Linden, N; Short, A J; Winter, A; Linden, Noah; Popescu, Sandu; Short, Anthony J.; Winter, Andreas
2006-01-01
We investigate the problem of "nonlocal" computation, in which separated parties must compute a function with nonlocally encoded inputs and output, such that each party individually learns nothing, yet together they compute the correct function output. We show that the best that can be done classically is a trivial linear approximation. Surprisingly, we also show that quantum entanglement provides no advantage over the classical case. On the other hand, generalized (i.e. super-quantum) nonlocal correlations allow perfect nonlocal computation. This gives new insights into the nature of quantum nonlocality and its relationship to generalised nonlocal correlations.
Secure Multi-party Quantum Computing
Crepeau, C; Smith, A; Crepeau, Claude; Gottesman, Daniel; Smith, Adam
2002-01-01
Secure multi-party computing, also called "secure function evaluation", has been extensively studied in classical cryptography. We consider the extension of this task to computation with quantum inputs and circuits. Our protocols are information-theoretically secure, i.e. no assumptions are made on the computational power of the adversary. For the weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to show how to perform any multi-party quantum computation as long as the number of dishonest players is less than n/6.
The case for biological quantum computer elements
Baer, Wolfgang; Pizzi, Rita
2009-05-01
An extension to vonNeumann's analysis of quantum theory suggests self-measurement is a fundamental process of Nature. By mapping the quantum computer to the brain architecture we will argue that the cognitive experience results from a measurement of a quantum memory maintained by biological entities. The insight provided by this mapping suggests quantum effects are not restricted to small atomic and nuclear phenomena but are an integral part of our own cognitive experience and further that the architecture of a quantum computer system parallels that of a conscious brain. We will then review the suggestions for biological quantum elements in basic neural structures and address the de-coherence objection by arguing for a self- measurement event model of Nature. We will argue that to first order approximation the universe is composed of isolated self-measurement events which guaranties coherence. Controlled de-coherence is treated as the input/output interactions between quantum elements of a quantum computer and the quantum memory maintained by biological entities cognizant of the quantum calculation results. Lastly we will present stem-cell based neuron experiments conducted by one of us with the aim of demonstrating the occurrence of quantum effects in living neural networks and discuss future research projects intended to reach this objective.
Quantum Computing and the Limits of the Efficiently Computable
CERN. Geneva
2015-01-01
I'll discuss how computational complexity---the study of what can and can't be feasibly computed---has been interacting with physics in interesting and unexpected ways. I'll first give a crash course about computer science's P vs. NP problem, as well as about the capabilities and limits of quantum computers. I'll then touch on speculative models of computation that would go even beyond quantum computers, using (for example) hypothetical nonlinearities in the Schrodinger equation. Finally, I'll discuss BosonSampling ---a proposal for a simple form of quantum computing, which nevertheless seems intractable to simulate using a classical computer---as well as the role of computational complexity in the black hole information puzzle.
Racing a quantum computer through Minkowski spacetime
International Nuclear Information System (INIS)
The Lorentzian length of a timelike curve connecting both endpoints of a computation in Minkowski spacetime is smaller than the Lorentzian length of the corresponding geodesic. In this talk, I will point out some properties of spacetime that allow an inertial classical computer to outperform a quantum one, at the completion of a long journey. We will focus on a comparison between the optimal quadratic Grover speed up from quantum computing and an n=2 speedup using classical computers and relativistic effects. These results are not practical as a new model of computation, but allow us to probe the ultimate limits physics places on computers.
Universal quantum computation with weakly integral anyons
Cui, Shawn X.; Hong, Seung-Moon; Wang, Zhenghan
2015-08-01
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum dimensions are integers. We analyze the computational power of the first non-abelian anyon system with only integral quantum dimensions—, the quantum double of . Since all anyons in have finite images of braid group representations, they cannot be universal for quantum computation by braiding alone. Based on our knowledge of the images of the braid group representations, we set up three qutrit computational models. Supplementing braidings with some measurements and ancillary states, we find a universal gate set for each model.
Resilient Quantum Computation Error Models and Thresholds
Knill, E H; Zurek, W H; Knill, Emanuel; Laflamme, Raymond; Zurek, Wojciech H.
1997-01-01
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.
KLM quantum computation with bosonic atoms
Popescu, S
2006-01-01
A Knill-Laflamme-Milburn (KLM) type quantum computation with bosonic neutral atoms or bosonic ions is suggested. Crucially, as opposite to other quantum computation schemes involving atoms (ions), no controlled interactions between atoms (ions) involving their internal levels are required. Versus photonic KLM computation this scheme has the advantage that single atom (ion) sources are more natural than single photon sources, and single atom (ion) detectors are far more efficient than single photon ones.
Reversible Mapping for Tree Structured Quantum Computation
Burkot, W
1997-01-01
A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer to a subspace of the available Hilbert space, where states are consistent with the problem constraints, can be done in polynomial time. The proposed mapping, together with the method of state reduction can be potentially used for solving NP-complete problems in polynomial time.
Models of Quantum Computers and Decoherence Problem
I. V. Volovich
1999-01-01
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one wants to build a quantum computer is the decoherence due to the coupling with the environment. We propose a possible solution of this problem by using a control of parameters of the system. This proposal is based on the analysis of the spin-boson Hamiltonian ...
Video Encryption and Decryption on Quantum Computers
Yan, Fei; Iliyasu, Abdullah M.; Venegas-Andraca, Salvador E.; Yang, Huamin
2015-08-01
A method for video encryption and decryption on quantum computers is proposed based on color information transformations on each frame encoding the content of the encoding the content of the video. The proposed method provides a flexible operation to encrypt quantum video by means of the quantum measurement in order to enhance the security of the video. To validate the proposed approach, a tetris tile-matching puzzle game video is utilized in the experimental simulations. The results obtained suggest that the proposed method enhances the security and speed of quantum video encryption and decryption, both properties required for secure transmission and sharing of video content in quantum communication.
Quantum Computation Using Optically Coupled Quantum Dot Arrays
Pradhan, Prabhakar; Anantram, M. P.; Wang, K. L.; Roychowhury, V. P.; Saini, Subhash (Technical Monitor)
1998-01-01
A solid state model for quantum computation has potential advantages in terms of the ease of fabrication, characterization, and integration. The fundamental requirements for a quantum computer involve the realization of basic processing units (qubits), and a scheme for controlled switching and coupling among the qubits, which enables one to perform controlled operations on qubits. We propose a model for quantum computation based on optically coupled quantum dot arrays, which is computationally similar to the atomic model proposed by Cirac and Zoller. In this model, individual qubits are comprised of two coupled quantum dots, and an array of these basic units is placed in an optical cavity. Switching among the states of the individual units is done by controlled laser pulses via near field interaction using the NSOM technology. Controlled rotations involving two or more qubits are performed via common cavity mode photon. We have calculated critical times, including the spontaneous emission and switching times, and show that they are comparable to the best times projected for other proposed models of quantum computation. We have also shown the feasibility of accessing individual quantum dots using the NSOM technology by calculating the photon density at the tip, and estimating the power necessary to perform the basic controlled operations. We are currently in the process of estimating the decoherence times for this system; however, we have formulated initial arguments which seem to indicate that the decoherence times will be comparable, if not longer, than many other proposed models.
Information free quantum bus for universal quantum computation
Devitt, S J; Hollenberg, L C L; Devitt, Simon J.; Greentree, Andrew D.; Hollenberg, Lloyd C.L.
2005-01-01
Long range transport of quantum information is of huge importance to the physical realisation of large scale quantum computers. This letter introduces a transport bus that deterministically mediates entanglment pairwise between isolated data qubits, while the bus itself never carries information. We demonstrate how this scheme generates standard two qubit operator measurements and its application to the preparation of linear cluster states and teleportation based universal computation.
Effective pure states for bulk quantum computation
Energy Technology Data Exchange (ETDEWEB)
Knill, E.; Chuang, I.; Laflamme, R.
1997-11-01
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) and Corey et al. (spatial averaging) for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla qubits and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high temperature and low temperature bulk quantum computing and analyze the signal to noise behavior of each.
Effective Pure States for Bulk Quantum Computation
Knill, E H; Laflamme, R; Knill, Emanuel; Chuang, Isaac; Laflamme, Raymond
1998-01-01
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) and Cory et al. (spatial averaging) for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla qubits and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high temperature and low temperature bulk quantum computing and analyze the signal to noise behavior of each.
Measurement Based Quantum Computation on Fractal Lattices
Directory of Open Access Journals (Sweden)
Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Principles of quantum computation and information
Benenti, Giuliano; Strini, Giuliano
2004-01-01
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.
Quantum computers on multiatomic ensembles in quantum electrodynamic cavity
Andrianov, S. N.; Moiseev, S. A.
2012-03-01
Schemes for the construction of quantum computers on multiatomic ensembles in quantum electrodynamic cavity are considered. With that, both encoding of physical qubits on each separate multiatomic ensemble and logical encoding of qubits on the pairs of ensembles are introduced. Possible constructions of swapping ( SWAP, sqrt {SWAP} ) and controlled swapping gates ( CSWAP) are analyzed. Mechanism of collective blockade and dynamical elimination procedure are proposed for realization of these gates. The comparison of the scheme solutions is carried out for the construction of quantum computer at using of physical and logical qubits.
Quantum Communication and Quantum Computation with Entangled Photons
Zeilinger, Anton
2006-06-01
Entangled photons provided the first evidence of a violation of Bell's inequality which implies a breakdown of the philosophical world-view of local realism. These experiments, having been extended over the years over ever longer distances, also provided the experimental foundation of the emerging field of quantum communication. There, quantum cryptography and quantum teleportation are key topics, which are already fairly advanced, being able to cover significant distances. Originally, it was thought that in a future quantum internet scheme, communication would be provided by photons while the local computers were to be realized with ions, atoms, atomic nuclei, solid state devices and the like. Interestingly, most recently the field of linear optics quantum computation has emerged with interesting possibilities and advantages.
Hamiltonian models of quantum computers which evolve quantum ballistically
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1996-12-31
Quantum computation is a subject of much recent interest. In much of the work in the literature quantum computers are described as built up from a sequence of unitary operators where each unitary operator carries out a stage of the overall quantum computation. The sequence and connection of the different unitary operators is provided presumably by some external agent which governs the overall process. However there is no description of a an overall Hamiltonian needed to give the actual quantum dynamics of the computation process. In this talk, earlier work by the author is followed in that simple, time independent Hamiltonians are used to describe quantum computation, and the Schroedinger evolution of the computation system is considered to be quantum ballistic. However, the definition of quantum ballistic evolution used here is more general than that used in the earlier work. In particular, the requirement that the step operator {ital T} associated with a process be a partial isometry, used in, is relaxed to require that {ital T} be a contraction operator. (An operator {ital T} is a partial isometry if the self-adjoint operators T{sup {dagger}}T and TT{sup {dagger}} are also projection operators.{ital T} is a contraction operator if {vert_bar}{vert_bar} {ital T} {vert_bar}{vert_bar} {<=} 1.) The main purpose of this talk is to investigate some consequences for quantum computation under this weaker requirement. It will be seen that system motion along discrete paths in a basis still occurs. However the motion occurs in ,the presence of potentials whose height and distribution along the path depends on {ital T} and the path states.
From quantum computation to quantum simulation: becoming more realistic
International Nuclear Information System (INIS)
The purpose of this talk is to introduce the basic tasks and goals of the EU FP7-project ''COQUIT (Collective quantum operations for information technology)''. Quantum systems are investigated which allow only a partial control by a constrained set of quantum operations. Typical examples are many particle quantum systems like cold atoms in optical lattices or other multi-atom ensembles, which can be manipulated collectively but not individually. Such restrictions are currently one of the biggest obstacles against working quantum computers. Instead of improving the corresponding experimental methods, we aim at a systematic study of the tasks which can be performed with currently available techniques. To this end we want to develop theoretical models which can on the one hand reflect the limitations of current experimental setups, but are on the other hand powerful enough to allow non-trivial practical applications. This point of view is new and complementary to most other research in quantum information science, where complete control over a small number of particles is assumed. One basic pillar of the COQUIT project is based on the concept of quantum simulation. Here a limited set of implementable operations is used to simulate physical properties of another quantum system. In this sense a quantum simulation device is a computational device for special purposes. We present the actual status of the project including new results and future perspectives.
Materials Frontiers to Empower Quantum Computing
Energy Technology Data Exchange (ETDEWEB)
Taylor, Antoinette Jane [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sarrao, John Louis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Richardson, Christopher [Laboratory for Physical Sciences, College Park, MD (United States)
2015-06-11
This is an exciting time at the nexus of quantum computing and materials research. The materials frontiers described in this report represent a significant advance in electronic materials and our understanding of the interactions between the local material and a manufactured quantum state. Simultaneously, directed efforts to solve materials issues related to quantum computing provide an opportunity to control and probe the fundamental arrangement of matter that will impact all electronic materials. An opportunity exists to extend our understanding of materials functionality from electronic-grade to quantum-grade by achieving a predictive understanding of noise and decoherence in qubits and their origins in materials defects and environmental coupling. Realizing this vision systematically and predictively will be transformative for quantum computing and will represent a qualitative step forward in materials prediction and control.
Faster quantum chemistry simulation on fault-tolerant quantum computers
Cody Jones, N.; Whitfield, James D.; McMahon, Peter L.; Yung, Man-Hong; Van Meter, Rodney; Aspuru-Guzik, Alán; Yamamoto, Yoshihisa
2012-11-01
Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error ?, arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log??) or O(log?log??) with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride.
Faster quantum chemistry simulation on fault-tolerant quantum computers
International Nuclear Information System (INIS)
Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems. Quantum teleportation plays a key role in these improvements and is used extensively as a computing resource. To improve execution time, we examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay–Kitaev algorithm (Dawson and Nielsen 2006 Quantum Inform. Comput. 6 81). For a given approximation error ?, arbitrary single-qubit gates can be produced fault-tolerantly and using a restricted set of gates in time which is O(log??) or O(log?log??); with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for lithium hydride. (paper)
Technologies for photonic quantum computing
International Nuclear Information System (INIS)
Full text: The photon is a near ideal carrier of quantum information showing little or no decoherence. The main sources of error become losses and small technical errors due to imperfect components. In the absence of single photon non-linearity we can use linear optics interference to make quantum gates albeit with limited efficiency. These optical quantum logic schemes require high efficiency sources of single and pair photons. These components in the quantum logic toolbox could be realised by exploiting wavelength scale engineering of optical structures. We discuss progress in developing high efficiency single photon sources based on periodic dielectric structures and generation of photon pairs in microstructured fibres. (author)
Applicability of Rydberg atoms to quantum computers
Ryabtsev, Igor I.; Tretyakov, Denis B.; Beterov, Ilya I.
2004-01-01
Applicability of Rydberg atoms to quantum computers is examined from experimental point of view. In many theoretical proposals appeared recently, excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interaction that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analyzed. We also present the results of modeling experiments on mic...
Can quantum mechanics help distributed computing?
Broadbent, Anne
2008-01-01
We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the survey is on communication complexity but we also address other distributed tasks.
Space-Efficient Simulation of Quantum Computers
Frank, Michael P.; Meyer-Baese, Uwe H.; Chiorescu, Irinel; Oniciuc, Liviu; van Engelen, Robert A.
2008-01-01
Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale platform with only a few gigabytes of main memory. However, more memory-efficient simulations are possible, requiring only polynomial or even linear space in the size of the quantum circuit being simulated. In this paper, we describe one s...
Universal Dephasing Control During Quantum Computation
Gordon, Goren; Kurizki, Gershon
2007-01-01
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, single- and two-qubit operators. We show that (a) tailoring multi-frequency gate pulses to the dephasing dynamics can increase fidelity; (b) cross-dephasing, introduced by entanglement, can be eliminated by appropri...
Superadiabatic Controlled Evolutions and Universal Quantum Computation.
Santos, Alan C; Sarandy, Marcelo S
2015-01-01
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts. PMID:26511064
Image segmentation on a quantum computer
Caraiman, Simona; Manta, Vasile I.
2015-05-01
In this paper, we address the field of quantum information processing and analyze the prospects of applying quantum computation concepts to image processing tasks. Specifically, we discuss the development of a quantum version for the image segmentation operation. This is an important technique that comes up in many image processing applications. We consider the threshold-based segmentation and show that a quantum circuit to achieve this operation can be built using a quantum oracle that implements the thresholding function. We discuss the circuit implementation of the oracle operator and provide examples of segmenting synthetic and real images. The main advantage of the quantum version for image segmentation over the classical approach is its speedup and is provided by the special properties of quantum information processing: superposition of states and inherent parallelism.
Quantum vs. Classical Communication and Computation
Buhrman, H; Wigderson, A; Buhrman, Harry; Cleve, Richard; Wigderson, Avi
1998-01-01
We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism. This allows us to obtain new positive and negative results. The positive results are novel quantum communication protocols that are built from nontrivial quantum algorithms via this simulation. These protocols, combined with (old and new) classical lower bounds, are shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) two-party communication complexity models. In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separation for the zero-error model. The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model. In particular, we show that the quadratic speed-up achieved by Grover for the OR function is...
CLASSICAL AND QUANTUM COMMUNICATIONS IN GRID COMPUTING
Directory of Open Access Journals (Sweden)
RODICA STERIAN
2010-10-01
Full Text Available The Quantum Crypted GRID Port developed under the D11-044 QUANTGRID project financed by the Romanian Center for Programme Management CNMP is presented: specifically the technology developed and the proprietary software used in the project. Quantum crypted communications eliminate the possibility of quantum-computer deciphering of messages (Shor's Lemma, while functioning with a public key exchange scheme – being secure by the very essence of quantum nature: any quantum state measured in any way collapses into one of its projections, thus it cannot be cloned and impossible to keep a copy thereof. The distribution of quantum public key is hence similar to the Vernam cipher (symmetrical – with secret key. The ongoing activities in this technology pertain to GRID communications through optical fiber and allow optimising the quantum security technology and experimenting proprietary algorithms for optimum data-volume/security for this new type of communications.
Superadiabatic Controlled Evolutions and Universal Quantum Computation
Santos, Alan C.; Sarandy, Marcelo S.
2015-01-01
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts. PMID:26511064
Reducing computational complexity of quantum correlations
Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal
2015-12-01
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures such as quantum discord and quantum work deficit in two qubits and higher-dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having nonpositive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.
Is the Brain a Quantum Computer?
Litt, Abninder; Eliasmith, Chris; Kroon, Frederick W.; Weinstein, Steven; Thagard, Paul
2006-01-01
We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic…
Directional Coupling for Quantum Computing and Communication
Nikolopoulos, Georgios M.
2008-01-01
We introduce the concept of directional coupling, i.e., the selective transfer of a state between adjacent quantum wires, in the context of quantum computing and short-distance communication. Our analysis rests upon a mathematical analogy between a dual-channel directional coupler and a composite spin system.
An introduction to quantum computing algorithms
Pittenger, Arthur O
2000-01-01
In 1994 Peter Shor [65] published a factoring algorithm for a quantum computer that finds the prime factors of a composite integer N more efficiently than is possible with the known algorithms for a classical com puter. Since the difficulty of the factoring problem is crucial for the se curity of a public key encryption system, interest (and funding) in quan tum computing and quantum computation suddenly blossomed. Quan tum computing had arrived. The study of the role of quantum mechanics in the theory of computa tion seems to have begun in the early 1980s with the publications of Paul Benioff [6]' [7] who considered a quantum mechanical model of computers and the computation process. A related question was discussed shortly thereafter by Richard Feynman [35] who began from a different perspec tive by asking what kind of computer should be used to simulate physics. His analysis led him to the belief that with a suitable class of "quantum machines" one could imitate any quantum system.
Halting in quantum Turing computation
Fouché, W. L.; J. Heidema; Jones, G.(Department of Physics, University of Warwick, Coventry, UK); Potgieter, P. H.
2007-01-01
The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of Ozawa as well as the objections raised by Myers, Kieu and Danos and others. Finally, the relationship of the halting scheme to the quest for a universal quantum Turing machine is considered.
Algorithms Bridging Quantum Computation and Chemistry
McClean, Jarrod Ryan
The design of new materials and chemicals derived entirely from computation has long been a goal of computational chemistry, and the governing equation whose solution would permit this dream is known. Unfortunately, the exact solution to this equation has been far too expensive and clever approximations fail in critical situations. Quantum computers offer a novel solution to this problem. In this work, we develop not only new algorithms to use quantum computers to study hard problems in chemistry, but also explore how such algorithms can help us to better understand and improve our traditional approaches. In particular, we first introduce a new method, the variational quantum eigensolver, which is designed to maximally utilize the quantum resources available in a device to solve chemical problems. We apply this method in a real quantum photonic device in the lab to study the dissociation of the helium hydride (HeH+) molecule. We also enhance this methodology with architecture specific optimizations on ion trap computers and show how linear-scaling techniques from traditional quantum chemistry can be used to improve the outlook of similar algorithms on quantum computers. We then show how studying quantum algorithms such as these can be used to understand and enhance the development of classical algorithms. In particular we use a tool from adiabatic quantum computation, Feynman's Clock, to develop a new discrete time variational principle and further establish a connection between real-time quantum dynamics and ground state eigenvalue problems. We use these tools to develop two novel parallel-in-time quantum algorithms that outperform competitive algorithms as well as offer new insights into the connection between the fermion sign problem of ground states and the dynamical sign problem of quantum dynamics. Finally we use insights gained in the study of quantum circuits to explore a general notion of sparsity in many-body quantum systems. In particular we use developments from the field of compressed sensing to find compact representations of ground states. As an application we study electronic systems and find solutions dramatically more compact than traditional configuration interaction expansions, offering hope to extend this methodology to challenging systems in chemical and material design.
Quantum Computational Representation of the Bosonic Oscillator
Jaroszkiewicz, G
2005-01-01
By the early eighties, Fredkin, Feynman, Minsky and others were exploring the notion that the laws of physics could be simulated with computers. Feynman's particular contribution was to bring quantum mechanics into the discussion and his ideas played a key role in the development of quantum computation. It was shown in 1995 by Barenco et al that all quantum computation processes could be written in terms of local operations and CNOT gates. We show how one of the most important of all physical systems, the quantized bosonic oscillator, can be rewritten in precisely those terms and therefore described as a quantum computational process, exactly in line with Feynman's ideas. We discuss single particle excitations and coherent states.
Iterated Gate Teleportation and Blind Quantum Computation
Pérez-Delgado, Carlos A.; Fitzsimons, Joseph F.
2015-06-01
Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraint only holds in limited scenarios, and show how to overcome it using a novel method of iterated gate teleportations. This technique enables drastic reductions in the communication required for distributed quantum protocols, extending beyond the blind computation setting. Applied to blind quantum computation, this technique offers significant efficiency improvements, and in some scenarios offers an exponential reduction in communication requirements.
Relativistic quantum chemistry on quantum computers.
Czech Academy of Sciences Publication Activity Database
Veis, Libor; Viš?ák, Jakub; Fleig, T.; Knecht, S.; Saue, T.; Visscher, L.; Pittner, Ji?í
2012-01-01
Ro?. 85, ?. 3 (2012), 030304. ISSN 1050-2947 R&D Projects: GA ?R GA203/08/0626 Institutional support: RVO:61388955 Keywords : simulation * algorithm * computation Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.042, year: 2012
Tempel, David Gabriel; Aspuru-Guzik, Alan
2011-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quan...
Basics of Quantum Computation (Part 1)
Rosinger, E E
2004-01-01
The aim of this textbook is to bridge in regard of quantum computation what proves to be a considerable threshold even to the usual science trained readership between the level of science popularization, and on the other hand, the presently available more encyclopedic textbooks. In this respect the present textbook is aimed to be a short, simple, rigorous and direct introduction, addressing itself only to quantum computation proper.
Quantum computation and Biological stress: A Hypothesis
Grover Monendra
2014-01-01
We propose that biological systems may behave as quantum computers.We have earlier hypothesized that patterns of quantum computation may be altered in stress and this leads to the change in the consciousness vector of biological systems. We further propose in this paper that the biological systems with a sufficient consciousness vector behave as objects which are entangled with the universal consciousness and as a consequence wormholes exist between the universal consciousness and the bio...
Quantum computation with trapped polar molecules
DeMille, D.
2001-01-01
We propose a novel physical realization of a quantum computer. The qubits are electric dipole moments of ultracold diatomic molecules, oriented along or against an external electric field. Individual molecules are held in a 1-D trap array, with an electric field gradient allowing spectroscopic addressing of each site. Bits are coupled via the electric dipole-dipole interaction. Using technologies similar to those already demonstrated, this design can plausibly lead to a quantum computer with ...
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
Biamonte, Jacob D.; Love, Peter J.
2007-01-01
It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the 2-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists working towards the realization of a universal adiabatic quantum computer. The model Hamiltonians pr...
Simulating quantum computers with probabilistic methods
Nest, M. Van den
2009-01-01
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate new classes of classically simulatable quantum circuits where standard techniques relying on the exact computation of measurement probabilities fail to provide efficient simulations. For example, we show how various concatenations of matchgate, Toffoli, Clif...
Noise thresholds for optical quantum computers
Dawson, Christopher M.; Haselgrove, Henry L.; Nielsen, Michael A.
2005-01-01
In this paper we numerically investigate the fault-tolerant threshold for optical cluster-state quantum computing. We allow both photon loss noise and depolarizing noise (as a general proxy for all local noise), and obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible for photon loss probabilities less than 0.003, and for depolarization probabilities less than 0.0001.
Noise thresholds for optical quantum computers.
Dawson, Christopher M; Haselgrove, Henry L; Nielsen, Michael A
2006-01-20
In this Letter we numerically investigate the fault-tolerant threshold for optical cluster-state quantum computing. We allow both photon loss noise and depolarizing noise (as a general proxy for all local noise), and obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible for photon loss probabilities <3 x 10(-3), and for depolarization probabilities <10(-4). PMID:16486553
Delayed commutation in quantum computer networks
Garcia-Escartin, Juan Carlos; Chamorro-Posada, Pedro
2005-01-01
In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communications. We propose a non-classical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes we can route the information after part of it has left the network ...
Accounting Principles are Simulated on Quantum Computers
Diep, Do Ngoc; Giang, Do Hoang
2005-01-01
The paper is devoted to a new idea of simulation of accounting by quantum computing. We expose the actual accounting principles in a pure mathematics language. After that we simulated the accounting principles on quantum computers. We show that all arbitrary accounting actions are exhausted by the described basic actions. The main problem of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation we use our constructed ...
More on Optical Holonomic Quantum Computer
Fujii, Kazuyuki
2000-01-01
We in this paper consider a further generalization of the (optical) holonomic quantum computation proposed by Zanardi and Rasetti (quant-ph/9904011), and reinforced by Fujii (quant-ph/9910069) and Pachos and Chountasis (quant-ph/9912093). We construct a quantum computational bundle on some parameter space, and calculate non-abelian Berry connections and curvatures explicitly in the special cases. Our main tool is unitary coherent operators based on Lie algebras su(n+1) and s...
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.
Universally Composable Quantum Multi-Party Computation
Unruh, Dominique
2009-01-01
The Universal Composability model (UC) by Canetti (FOCS 2001) allows for secure composition of arbitrary protocols. We present a quantum version of the UC model which enjoys the same compositionality guarantees. We prove that in this model statistically secure oblivious transfer protocols can be constructed from commitments. Furthermore, we show that every statistically classically UC secure protocol is also statistically quantum UC secure. Such implications are not known for other quantum security definitions. As a corollary, we get that quantum UC secure protocols for general multi-party computation can be constructed from commitments.
Why now is the right time to study quantum computing
Harrow, Aram W.
2014-01-01
Quantum computing is a good way to justify difficult physics experiments. But until quantum computers are built, do computer scientists need to know anything about quantum information? In fact, quantum computing is not merely a recipe for new computing devices, but a new way of looking at the world that has been astonishingly intellectually productive. In this article, I'll talk about where quantum computing came from, what it is, and what we can learn from it.
Computing the Exit Complexity of Knowledge in Distributed Quantum Computers
Abbas, M. A.
2013-01-01
Distributed Quantum computers abide from the exit complexity of the knowledge. The exit complexity is the accrue of the nodal information needed to clarify the total egress system with deference to a distinguished exit node. The core objective of this paper is to compile an arrogant methodology for assessing the exit complexity of the knowledge in distributed quantum computers. The proposed methodology is based on contouring the knowledge using the unlabeled binary trees, hence building an b...
Mathematical Models of Contemporary Elementary Quantum Computing Devices
Chen, G.; Church, D. A.; Englert, B. -G.; Zubairy, M. S.
2003-01-01
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any n-bit unitary operation can be carried out by concatenations of 1-bit and 2-bit elementary quantum gates. Three contemporary quantum devices--cavity QED, ion traps and quantum dots--have been widely regarded as perhaps the most promising ...
Classical signal-flow in cluster-state quantum computation
Oshima, Kazuto
2009-01-01
We study concretely how classical signals should be processed in quantum cluster-state computation. Deforming corresponding quantum teleportation circuit, we find a simple rule of a classical signal-flow to obtain correct quantum computation results.
Quantum Computing and Shor`s Factoring Algorithm
Volovich, Igor V.
2001-01-01
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm. Factoring integers. NP-complete problems.
Stabilisation of quantum computations by symmetrisation
Barenco, A; Ekert, A K; Jozsa, R; Macchiavello, C; Barenco, Adriano; Deutsch, David; Ekert, Artur; Jozsa, Richard; Macchiavello, Chiara
1996-01-01
We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into \\cal SYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting \\cal SYM--projection and discuss the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.
Theory of fault-tolerant quantum computation
Energy Technology Data Exchange (ETDEWEB)
Gottesman, D. [California Institute of Technology, Pasadena, California 91125 (United States)]|[Los Alamos National Laboratories, Los Alamos, New Mexico 87545 (United States)
1998-01-01
In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-quantum-bit code. {copyright} {ital 1998} {ital The American Physical Society}
Brain-Computer Interfaces and Quantum Robots
Pessa, Eliano
2009-01-01
The actual (classical) Brain-Computer Interface attempts to use brain signals to drive suitable actuators performing the actions corresponding to subject's intention. However this goal is not fully reached, and when BCI works, it does only in particular situations. The reason of this unsatisfactory result is that intention cannot be conceived simply as a set of classical input-output relationships. It is therefore necessary to resort to quantum theory, allowing the occurrence of stable coherence phenomena, in turn underlying high-level mental processes such as intentions and strategies. More precisely, within the context of a dissipative Quantum Field Theory of brain operation it is possible to introduce generalized coherent states associated, within the framework of logic, to the assertions of a quantum metalanguage. The latter controls the quantum-mechanical computing corresponding to standard mental operation. It thus become possible to conceive a Quantum Cyborg in which a human mind controls, through a qu...
Natural and artificial atoms for quantum computation
International Nuclear Information System (INIS)
Remarkable progress towards realizing quantum computation has been achieved using natural and artificial atoms as qubits. This paper presents a brief overview of the current status of different types of qubits. On the one hand, natural atoms (such as neutral atoms and ions) have long coherence times, and could be stored in large arrays, providing ideal 'quantum memories'. On the other hand, artificial atoms (such as superconducting circuits or semiconductor quantum dots) have the advantage of custom-designed features and could be used as 'quantum processing units'. Natural and artificial atoms can be coupled with each other and can also be interfaced with photons for long-distance communications. Hybrid devices made of natural/artificial atoms and photons may provide the next-generation design for quantum computers.
Elements of quantum computing history, theories and engineering applications
Akama, Seiki
2015-01-01
A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's, and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation, and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers. This book provides a quick introduction to quantum computing for readers who have no backgrounds of both theory of computation and quantum mechanics. “Elements of Quantum Computing” presents the history, theories, and engineering applications of quantum computing. The book is suitable to computer scientists, physicist, and software engineers.
Hamiltonian quantum computer in one dimension
Wei, Tzu-Chieh; Liang, John C.
2015-12-01
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach is called the Hamiltonian quantum computation and it includes, for example, the continuous-time quantum cellular automata and the universal quantum walk. We consider one spatial dimension and study the compromise between the locality k and the local Hilbert space dimension d . For geometrically 2-local (i.e., k =2 ), it is known that d =8 is already sufficient for universal quantum computation but the Hamiltonian is not translationally invariant. As the locality k increases, it is expected that the minimum required d should decrease. We provide a construction of a Hamiltonian quantum computer for k =3 with d =5 . One implication is that simulating one-dimensional chains of spin-2 particles is BQP-complete (BQP denotes "bounded error, quantum polynomial time"). Imposing translation invariance will increase the required d . For this we also construct another 3-local (k =3 ) Hamiltonian that is invariant under translation of a unit cell of two sites but that requires d to be 8.
Quantum algorithms for computational nuclear physics
Directory of Open Access Journals (Sweden)
Viš?ák Jakub
2015-01-01
Full Text Available While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei for its possible practical realization on a real quantum computer.
Quantum algorithms for computational nuclear physics
Viš?ák, Jakub
2015-07-01
While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials) have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer) of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei) for its possible practical realization on a real quantum computer.
Quantum computation and pseudo-telepathic games
Bub, Jeffrey
2010-01-01
A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information-processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. I also introduce the notion of 'pseudo-telepathic' games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players' correlated responses in a game).
Simulating physical phenomena with a quantum computer
Ortiz, Gerardo
2003-03-01
In a keynote speech at MIT in 1981 Richard Feynman raised some provocative questions in connection to the exact simulation of physical systems using a special device named a ``quantum computer'' (QC). At the time it was known that deterministic simulations of quantum phenomena in classical computers required a number of resources that scaled exponentially with the number of degrees of freedom, and also that the probabilistic simulation of certain quantum problems were limited by the so-called sign or phase problem, a problem believed to be of exponential complexity. Such a QC was intended to mimick physical processes exactly the same as Nature. Certainly, remarks coming from such an influential figure generated widespread interest in these ideas, and today after 21 years there are still some open questions. What kind of physical phenomena can be simulated with a QC?, How?, and What are its limitations? Addressing and attempting to answer these questions is what this talk is about. Definitively, the goal of physics simulation using controllable quantum systems (``physics imitation'') is to exploit quantum laws to advantage, and thus accomplish efficient imitation. Fundamental is the connection between a quantum computational model and a physical system by transformations of operator algebras. This concept is a necessary one because in Quantum Mechanics each physical system is naturally associated with a language of operators and thus can be considered as a possible model of quantum computation. The remarkable result is that an arbitrary physical system is naturally simulatable by another physical system (or QC) whenever a ``dictionary'' between the two operator algebras exists. I will explain these concepts and address some of Feynman's concerns regarding the simulation of fermionic systems. Finally, I will illustrate the main ideas by imitating simple physical phenomena borrowed from condensed matter physics using quantum algorithms, and present experimental quantum simulations performed in a liquid NMR QC.
Models to Reduce the Complexity of Simulating a Quantum Computer
Obenland, Kevin M.; Despain, Alvin M.
1997-01-01
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation is a useful tool for determining the feasibility of quantum computers in the presence of errors. The size of a quantum computer that can be simulat ed is small because faithfully modeling a quantum computer requires an exponential amount of storage and num...
Diagonal quantum circuits: their computational power and applications
Nakata, Yoshifumi; Murao, Mio
2014-01-01
Diagonal quantum circuits are quantum circuits comprising only diagonal gates in the computational basis. In spite of a classical feature of diagonal quantum circuits in the sense of commutativity of all gates, their computational power is highly likely to outperform classical one and they are exploited for applications in quantum informational tasks. We review computational power of diagonal quantum circuits and their applications. We focus on the computational power of instantaneous quantum...
Quantum-State-Engineering for Spin-Quantum-Computing
Heidebrecht, Andreas
2006-01-01
The subject of this thesis are experimental procedures for preparation, manipulation, and detection of specific quantum states of spin systems in the context of quantum computing. Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) methods were used. The systems studied were small molecules in liquid state, small molecules embedded in a liquid crystal matrix, and paramagnetic centers in single crystals. The nuclear 19F spins of 2,3,4-Trifluoroaniline were u...
Diamond NV centers for quantum computing and quantum networks
Lilian Childress; Ronald Hanson
2013-01-01
The exotic features of quantum mechanics have the potential to revolutionize information technologies. Using superposition and entanglement, a quantum processor could efficiently tackle problems inaccessible to current-day computers. Nonlocal correlations may be exploited for intrinsically secure communication across the globe. Finding and controlling a physical system suitable for fulfi lling these promises is one of the greatest challenges of our time. The nitrogen-vacancy (NV) center in di...
Quantum Computing with Electron Spins in Quantum Dots
L. M. K. Vandersypen; Hanson, R.; van Beveren, L. H. Willems; Elzerman, J. M.; Greidanus, J.S.; Franceschi, S; Kouwenhoven, L. P.
2002-01-01
We present a set of concrete and realistic ideas for the implementation of a small-scale quantum computer using electron spins in lateral GaAs/AlGaAs quantum dots. Initialization is based on leads in the quantum Hall regime with tunable spin-polarization. Read-out hinges on spin-to-charge conversion via spin-selective tunneling to or from the leads, followed by measurement of the number of electron charges on the dot via a charge detector. Single-qubit manipulation relies on...
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
Quantum state transition diagram: a bridge from classical computing to quantum computing
Hook, Loyd R., IV; Lee, Samuel C.
2010-04-01
Very few papers have been written on the topic of a quantum version of the finite state machine, (or finite state automata). Furthermore, these papers only serve to define what a quantum finite state machine might be in the mathematical sense using the early languages of Turing machines. This paper seeks to further develop the notion of a quantum finite state machine (FSM) using constructs developed for the classical FSM and utilized for classical FSM design. In particular the quantum state transition diagram (QSTD) is constructed to further the understanding and realization of quantum finite state machines and quantum computers.
Quantum computing with black-box quantum subroutines
International Nuclear Information System (INIS)
In classical computation a subroutine is treated as a black box and we do not need to know its exact physical implementation to use it. A complex problem can be decomposed into smaller problems using such modularity. We show that quantum mechanically applying an unknown quantum process as a subroutine is impossible, and this restricts computation models such as DQC1 from operating on unknown inputs. We present a method to avoid this situation for certain computational problems and apply to a modular version of Shor's factoring algorithm. We examine how quantum entanglement and discord fare in this implementation. In this way we are able to study the role of discord in Shor's factoring algorithm.
Construction of a universal quantum computer
International Nuclear Information System (INIS)
We construct a universal quantum computer following Deutsch's original proposal of a universal quantum Turing machine (UQTM). Like Deutsch's UQTM, our machine can emulate any classical Turing machine and can execute any algorithm that can be implemented in the quantum gate array framework but under the control of a quantum program, and hence is universal. We present the architecture of the machine, which consists of a memory tape and a processor and describe the observables that comprise the registers of the processor and the instruction set, which includes a set of operations that can approximate any unitary operation to any desired accuracy and hence is quantum computationally universal. We present the unitary evolution operators that act on the machine to achieve universal computation and discuss each of them in detail and specify and discuss explicit program halting and concatenation schemes. We define and describe a set of primitive programs in order to demonstrate the universal nature of the machine. These primitive programs facilitate the implementation of more complex algorithms and we demonstrate their use by presenting a program that computes the NAND function, thereby also showing that the machine can compute any classically computable function.
Construction of a universal quantum computer
Lagana, Antonio A.; Lohe, M. A.; von Smekal, Lorenz
2009-05-01
We construct a universal quantum computer following Deutsch’s original proposal of a universal quantum Turing machine (UQTM). Like Deutsch’s UQTM, our machine can emulate any classical Turing machine and can execute any algorithm that can be implemented in the quantum gate array framework but under the control of a quantum program, and hence is universal. We present the architecture of the machine, which consists of a memory tape and a processor and describe the observables that comprise the registers of the processor and the instruction set, which includes a set of operations that can approximate any unitary operation to any desired accuracy and hence is quantum computationally universal. We present the unitary evolution operators that act on the machine to achieve universal computation and discuss each of them in detail and specify and discuss explicit program halting and concatenation schemes. We define and describe a set of primitive programs in order to demonstrate the universal nature of the machine. These primitive programs facilitate the implementation of more complex algorithms and we demonstrate their use by presenting a program that computes the NAND function, thereby also showing that the machine can compute any classically computable function.
Qubus ancilla-driven quantum computation
International Nuclear Information System (INIS)
Hybrid matter-optical systems offer a robust, scalable path to quantum computation. Such systems have an ancilla which acts as a bus connecting the qubits. We demonstrate how using a continuous variable qubus as the ancilla provides savings in the total number of operations required when computing with many qubits
Qubus ancilla-driven quantum computation
Energy Technology Data Exchange (ETDEWEB)
Brown, Katherine Louise [School of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70808, United States and School of Physics and Astronomy, University of Leeds, LS2 9JT (United Kingdom); De, Suvabrata; Kendon, Viv [School of Physics and Astronomy, University of Leeds, LS2 9JT (United Kingdom); Munro, Bill [National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan and NTT Basic Research Laboratories, 3-1, Morinosato Wakamiya Atsugi-shi, Kanagawa 243-0198 (Japan)
2014-12-04
Hybrid matter-optical systems offer a robust, scalable path to quantum computation. Such systems have an ancilla which acts as a bus connecting the qubits. We demonstrate how using a continuous variable qubus as the ancilla provides savings in the total number of operations required when computing with many qubits.
Discrete Cosine Transforms on Quantum Computers
Klappenecker, Andreas; Roetteler, Martin
2001-01-01
A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on a quantum computer, whereas ...
Theory of Quantum Computing and Communication
Fortnow, L
2002-01-01
A workshop sponsored by NSF C-CR and organized by the Center for Discrete Math and Theoretical Computer Science (DIMACS) was held at Elmsford, New York, January 17-18, 2002 where we had several discussions that gave structure to this report. The workshop immediately followed the Fifth Annual Quantum Information Processing Workshop that was held January 14-17 at IBM Yorktown. This is the report from that workshop. The report recommends that the NSF Division of Computer-Communications Research (C-CR) develop a new initiative in "Theory of Quantum Computing and Communication" and describes several research directions that this initiative could support.
Biologically inspired path to quantum computer
Ogryzko, Vasily; Ozhigov, Yuri
2014-12-01
We describe an approach to quantum computer inspired by the information processing at the molecular level in living cells. It is based on the separation of a small ensemble of qubits inside the living system (e.g., a bacterial cell), such that coherent quantum states of this ensemble remain practically unchanged for a long time. We use the notion of a quantum kernel to describe such an ensemble. Quantum kernel is not strictly connected with certain particles; it permanently exchanges atoms and molecules with the environment, which makes quantum kernel a virtual notion. There are many reasons to expect that the state of quantum kernel of a living system can be treated as the stationary state of some Hamiltonian. While the quantum kernel is responsible for the stability of dynamics at the time scale of cellular life, at the longer inter-generation time scale it can change, varying smoothly in the course of biological evolution. To the first level of approximation, quantum kernel can be described in the framework of qubit modification of Jaynes-Cummings-Hubbard model, in which the relaxation corresponds to the exchange of matter between quantum kernel and the rest of the cell and is represented as Lindblad super-operators.
Bethe ansatz, quantum computers, and unitary geometry
Energy Technology Data Exchange (ETDEWEB)
Lulek, T [Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, Department of Physics, Powstancow Warszawy 6, 35-959 Rzeszow (Poland)], E-mail: tadlulek@prz.edu.pl
2008-03-01
The one-dimensional ring of N magnetic nodes, each node with the spin 1/2, can be seen as a faithful prototype of a quantum computer with N qubits. We point out here some analogies between typical problems and known solutions of the Heisenberg model of a magnet on this ring, and the related questions posed within the midst of quantum information processing. In particular, we relate such notions as the memory, gates, or entanglement of quantum states with exact results of Bethe Ansatz, expressed in combinatoric terms of rigged string configurations. A promising and transparent interpretation of relation between Bethe Ansatz and quantum computation can be provided by the unitary geometry of Schwinger, presented in our previous SSPCM schools by prof. Vourdas.
Space-Efficient Simulation of Quantum Computers
Frank, Michael P; Chiorescu, Irinel; Oniciuc, Liviu; van Engelen, Robert A
2008-01-01
Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale platform with only a few gigabytes of main memory. However, more memory-efficient simulations are possible, requiring only polynomial or even linear space in the size of the quantum circuit being simulated. In this paper, we describe one such technique, which was recently implemented at FSU in the form of a C++ program called SEQCSIM, which we releasing publicly. We also discuss the potential benefits of this simulation in quantum computing research and education, and outline some possible directions for further progress.
Factoring in a dissipative quantum computer
Miquel, C; Perazzo, R P J; Miquel, Cesar; Paz, Juan Pablo; Perazzo, Roberto
1996-01-01
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.
Accelerating commutation circuits in quantum computer networks
Jiang, Min; Huang, Xu; Chen, Xiaoping; Zhang, Zeng-ke
2012-12-01
In a high speed and packet-switched quantum computer network, a packet routing delay often leads to traffic jams, becoming a severe bottleneck for speeding up the transmission rate. Based on the delayed commutation circuit proposed in Phys. Rev. Lett. 97, 110502 (2006), we present an improved scheme for accelerating network transmission. For two more realistic scenarios, we utilize the characteristic of a quantum state to simultaneously implement a data switch and transmission that makes it possible to reduce the packet delay and route a qubit packet even before its address is determined. This circuit is further extended to the quantum network for the transmission of the unknown quantum information. The analysis demonstrates that quantum communication technology can considerably reduce the processing delay time and build faster and more efficient packet-switched networks.
Analogue Quantum Computers for Data Analysis
Vlasov, Alexander Yu.
1998-01-01
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 effectively in comp...
Consequences and Limitations of Conventional Computers and their Solutions through Quantum Computers
Nilesh BARDE; Deepak THAKUR; Pranav BARDAPURKAR; Sanjaykumar DALVI
2012-01-01
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 peri...
Consequences and Limitations of Conventional Computers and their Solutions through Quantum Computers
Sanjaykumar DALVI; Pranav BARDAPURKAR; Nilesh BARDE; Deepak THAKUR
2011-01-01
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 peri...
Quantum Computers: A New Paradigm in Information Technology
Raisinghani, Mahesh S.
2001-01-01
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...
Quantum computing by pairing trapped ultracold ions
Mang, F; Kelin, G; Lei, S; Mang, Feng; Xiwen, Zhu; Kelin, Gao; Lei, Shi
2000-01-01
The superpositional wave function oscillations for finite-time implementation of quantum algorithms modifies the desired interference required for quantum computing. We propose a scheme with trapped ultracold ion-pairs being qubits to diminish the detrimental effect of the wave function oscillations, and apply the scheme to the two-qubit Grover's search. It can be also found that the qubits in our scheme are more robust against the decoherence caused by the environment, and the model is scalable.
Quantum Theory of Computation and Relativistic Physics
Vlasov, A Yu
1997-01-01
In the e-print is discussed a few steps to introducing of "vocabulary" of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as models in QTI&C is tested by usual relativistic tools (transformation properties of wave vectors, etc.). Massless and charged massive particles with spin 1/2 is considered. Field theory is also discussed briefly.
Qdensity - a Mathematica Quantum Computer Simulation
Juliá-Díaz, B.; Burdis, J. M.; Tabakin, F.
2005-01-01
This Mathematica 5.2 package~\\footnote{QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY} 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 qua...
Interconnection Networks for Scalable Quantum Computers
Isailovic, Nemanja; Patel, Yatish; Whitney, Mark; Kubiatowicz, John
2006-01-01
We show that the problem of communication in a quantum computer reduces to constructing reliable quantum channels by distributing high-fidelity EPR pairs. We develop analytical models of the latency, bandwidth, error rate and resource utilization of such channels, and show that 100s of qubits must be distributed to accommodate a single data communication. Next, we show that a grid of teleportation nodes forms a good substrate on which to distribute EPR pairs. We also explore the control requi...
Local Search Methods for Quantum Computers
Hogg, Tad; YANIK, Mehmet
1998-01-01
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 somewhat less effecti...
Entanglement and Quantum Computation: An Overview
Energy Technology Data Exchange (ETDEWEB)
Perez, R.B.
2000-06-27
This report presents a selective compilation of basic facts from the fields of particle entanglement and quantum information processing prepared for those non-experts in these fields that may have interest in an area of physics showing counterintuitive, ''spooky'' (Einstein's words) behavior. In fact, quantum information processing could, in the near future, provide a new technology to sustain the benefits to the U.S. economy due to advanced computer technology.
Optical quantum computer based on RDS crystal
Sazonova, Z. S.; Singh, Ranjit
2001-01-01
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 cr...
Quantum computing by pairing trapped ultracold ions
Mang, Feng; Xiwen, Zhu; Kelin, Gao; Lei, Shi
2000-01-01
The superpositional wave function oscillations for finite-time implementation of quantum algorithms modifies the desired interference required for quantum computing. We propose a scheme with trapped ultracold ion-pairs being qubits to diminish the detrimental effect of the wave function oscillations, and apply the scheme to the two-qubit Grover's search. It can be also found that the qubits in our scheme are more robust against the decoherence caused by the environment, and ...
Universal Dephasing Control During Quantum Computation
Gordon, Goren
2007-01-01
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, single- and two-qubit operators. We show that (a) tailoring multi-frequency gate pulses to the dephasing dynamics can increase fidelity; (b) cross-dephasing, introduced by entanglement, can be eliminated by appropriate control fields; (c) counter-intuitively and contrary to previous schemes, one can increase the gate duration, while simultaneously increasing the total gate fidelity.
Local Search Methods for Quantum Computers
Hogg, T; Hogg, Tad; Yanik, Mehmet
1998-01-01
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 somewhat less effective at exploiting problem structure than incremental quantum methods, in spite of the much smaller search space used by the local method.
Quantum learning for a quantum lattice gas computer
Behrman, Elizabeth; Steck, James
2015-03-01
Quantum lattice gas is the logical generalization of quantum cellular automata. In low energy the dynamics are well described by the Gross-Pitaevskii equation in the mean field limit, which is an effective nonlinear interaction model of a Bose-Einstein condensate. In previous work, we have shown in simulation that both spatial and temporal models of quantum learning computers can be used to ``design'' non-trivial quantum algorithms. The advantages of quantum learning over the usual practice of using quantum gate building blocks are, first, the rapidity with which the problem can be solved, without having to decompose the problem; second, the fact that our technique can be used readily even when the problem, or the operator, is not well understood; and, third, that because the interactions are a natural part of the physical system, connectivity is automatic. The advantage to quantum learning obviously grows with the size and the complexity of the problem. We develop and present our learning algorithm as applied to the mean field lattice gas equation, and present a few preliminary results.
Quantum learning in a quantum lattice gas computer
Behrman, Elizabeth; Steck, James
2015-04-01
Quantum lattice gas is the logical generalization of quantum cellular automata. At low energy the dynamics are well described by the Gross-Pitaevskii equation in the mean field limit, which is an effective nonlinear interaction model of a Bose-Einstein condensate. In previous work, we have shown in simulation that both spatial and temporal models of quantum learning computers can be used to ``design'' non-trivial quantum algorithms. The advantages of quantum learning over the usual practice of using quantum gate building blocks are, first, the rapidity with which the problem can be solved, without having to decompose the problem; second, the fact that our technique can be used readily even when the problem, or the operator, is not well understood; and, third, that because the interactions are a natural part of the physical system, connectivity is automatic. The advantage to quantum learning obviously grows with the size and the complexity of the problem. We develop and present our learning algorithm as applied to the mean field lattice gas equation, and present a few preliminary results.
Neuromorphic quantum computation with energy dissipation
International Nuclear Information System (INIS)
Real parallel computing with a quantum computer attracts vast interest due to its extreme high potential. We propose a neuromorphic quantum computation algorithm based on an adiabatic Hamiltonian evolution with energy dissipation. This algorithm can be applied to problems if a cost function can be expressed in a quadratic form. This requirement results from the fact that our Hamiltonian is designed by following a method similar to an artificial neural network (ANN). The state of an ANN is often trapped at local minima, and the network outputs an error. Since the state of a quantum system with the proposed algorithm is always in the ground state according to the adiabatic theorem, it is not necessary to be concerned that the quantum state is trapped at local minima. However, there is no guarantee that a quantum algorithm based on an adiabatic Hamiltonian evolution with degeneration or level crossing is successfully executed. We show successful numerical simulation results with the proposed algorithm by introducing energy dissipation to keep the quantum state staying in the ground state, and then we show an application to the n-queen problem, which is one of the combinatorial optimization problems
Simulating Grover's Quantum Search in a Classical Computer
Ningtyas, D. K.; A.B. Mutiara
2010-01-01
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of computing science, much effort is being put into the development of new quantum algorithms. One of quantum algorithms is Grover algorithm, which is used for searching an element in an unstructured list of N elements with quadratic speed-up over cl...
Methodological testing: Are fast quantum computers illusions?
Energy Technology Data Exchange (ETDEWEB)
Meyer, Steven [Tachyon Design Automation, San Francisco, CA (United States)
2013-07-01
Popularity of the idea for computers constructed from the principles of QM started with Feynman's 'Lectures On Computation', but he called the idea crazy and dependent on statistical mechanics. In 1987, Feynman published a paper in 'Quantum Implications - Essays in Honor of David Bohm' on negative probabilities which he said gave him cultural shock. The problem with imagined fast quantum computers (QC) is that speed requires both statistical behavior and truth of the mathematical formalism. The Swedish Royal Academy 2012 Nobel Prize in physics press release touted the discovery of methods to control ''individual quantum systems'', to ''measure and control very fragile quantum states'' which enables ''first steps towards building a new type of super fast computer based on quantum physics.'' A number of examples where widely accepted mathematical descriptions have turned out to be problematic are examined: Problems with the use of Oracles in P=NP computational complexity, Paul Finsler's proof of the continuum hypothesis, and Turing's Enigma code breaking versus William tutte's Colossus. I view QC research as faith in computational oracles with wished for properties. Arther Fine's interpretation in 'The Shaky Game' of Einstein's skepticism toward QM is discussed. If Einstein's reality as space-time curvature is correct, then space-time computers will be the next type of super fast computer.
Random Numbers and Quantum Computers
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms. PMID:22553483
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
Quantum Computation and Quantum Information: Are They Related to Quantum Paradoxology?
Gyftopoulos, Elias P.; von Spakovsky, Michael R.
2004-01-01
We review both the Einstein, Podolsky, Rosen (EPR) paper about the completeness of quantum theory, and Schrodinger's responses to the EPR paper. We find that both the EPR paper and Schrodinger's responses, including the cat paradox, are not consistent with the current understanding of quantum theory and thermodynamics. Because both the EPR paper and Schrodinger's responses play a leading role in discussions of the fascinating and promising fields of quantum computation and quantum information...
Towards universal quantum computation through relativistic motion
Bruschi, David Edward; Kok, Pieter; Johansson, Göran; Delsing, Per; Fuentes, Ivette
2013-01-01
We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconducting circuits where tunable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes.
Generalized GHZ State and Distributed Quantum Computing
Yimsiriwattana, A
2004-01-01
A key problem in quantum computing is finding a viable technological path toward the creation of a scalable quantum computer. One possible approach toward solving part of this problem is distributed computing, which provides an effective way of utilizing a network of limited capacity quantum computers. In this paper, we present two primitive operations, cat-entangler and cat-disentangler, which in turn can be used to implement non-local operations, e.g. non-local CNOT and quantum teleportation. We also show how to establish an entangled pair, and use entangled pairs to efficiently create a generalized GHZ state. Furthermore, we present procedures which allow us to reuse channel qubits in a sequence of non-local operations. These non-local operations work on the principle that a cat-like state, created by cat-entangler, can be used to distribute a control qubit among multiple computers. Using this principle, we show how to efficiently implement non-local control operations in many situation, including a parall...
Adiabatic graph-state quantum computation
International Nuclear Information System (INIS)
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 H-dot 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. (paper)
Mizel, Ari
2003-01-01
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.
Quantum Computing in Non Euclidean Geometry
Resconi, Germano
2009-01-01
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics a...
Quantum pathology of static internal imperfections in flawed quantum computers
Energy Technology Data Exchange (ETDEWEB)
Cetinbas, Murat [Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, V5A 1S6 (Canada)], E-mail: cetinbas@sfu.ca; Wilkie, Joshua [Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, V5A 1S6 (Canada)], E-mail: wilkie@sfu.ca
2007-10-22
Even in the absence of external influences the operability of a quantum computer (QC) is not guaranteed because of the effects of residual one- and two-body imperfections. Here we investigate how these internal flaws affect the performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC. First we find that the performance of the CNOT gate is considerably better when the two-body imperfections are strong. Secondly, we find that the largest source of error is due to a coherent shift rather than decoherence or dissipation. Our results suggest that the problem of internal imperfections should be given much more attention in designing scalable QC architectures.
Quantum pathology of static internal imperfections in flawed quantum computers
Cetinbas, Murat; Wilkie, Joshua
2007-01-01
Even in the absence of external influences the operability of a quantum computer (QC) is not guaranteed because of the effects of residual one- and two-body imperfections. Here we investigate how these internal flaws affect the performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC. First we find that the performance of the CNOT gate is considerably better when the two-body imperfections are strong. Secondly, we find that the largest source of error is due to a coherent ...
Quantum pathology of static internal imperfections in flawed quantum computers
Cetinbas, Murat
2007-01-01
Even in the absence of external influences the operability of a quantum computer (QC) is not guaranteed because of the effects of residual one- and two-body imperfections. Here we investigate how these internal flaws affect the performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC. First we find that the performance of the CNOT gate is considerably better when the two-body imperfections are strong. Secondly, we find that the largest source of error is due to a coherent shift rather than decoherence or dissipation. Our results suggest that the problem of internal imperfections should be given much more attention in designing scalable QC architectures.
Quantum computer games: Schrödinger cat and hounds
Gordon, Michal; Gordon, Goren
2012-05-01
The quantum computer game 'Schrödinger cat and hounds' is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. 'Schrödinger cat and hounds' demonstrates the effects of superposition, destructive and constructive interference, measurements and entanglement. More advanced concepts, like particle-wave duality and decoherence, can also be taught using the game as a model. The game that has an optimal solution in the classical version, can have many different solutions and a new balance of powers in the quantum world. Game-aided lectures were given to high-school students which showed that it is a valid and entertaining teaching platform.
Temporal resources for global quantum computing architectures
Scientific Electronic Library Online (English)
Juan D., Jaramillo; John H., Reina.
2008-12-01
Full Text Available 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.
Quantum computing implementations with neutral particles
DEFF Research Database (Denmark)
Negretti, Antonio; Treutlein, Philipp
2011-01-01
We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both single- and two-qubit gate implementations. We focus our discussion mainly on collisional quantum gates, which are best suited for atom-chip-like devices, as well as on gate proposals conceived for optical lattices. Additionally, we analyze schemes both for cold atoms confined in optical cavities and hybrid approaches to entanglement generation, and we show how optimal control theory might be a powerful tool to enhance the speed up of the gate operations as well as to achieve high fidelities required for fault tolerant quantum computation.
A surface code quantum computer in silicon
Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.
2015-01-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310
A surface code quantum computer in silicon.
Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L
2015-10-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310
Industrial Superconducting Quantum Computer Development in Canada
Rose, Geordie
2002-05-01
Quantum computation is one of the most active areas of research in academia. Nearly every university in the world that has a science department has researchers who are working on either trying to build hardware or develop algorithms for these machines. In this talk I will describe D-Wave's goals and achievements in assembling a global research network, centered in Canada, whose purpose is the development of superconducting quantum computer hardware. In addition I will describe the technical approach that we are concentrating on, involving cuprate-based flux qubits and niobium RSFQ control circuitry. Finally I will introduce a very important application of these machines, namely their use as simulators of other quantum systems, in the context of human pharmaceutical drug and vaccine design.
Semiclassical Fourier transform for quantum computation
Griffiths, R B; Griffiths, Robert B; Niu, Chi Sheng
1995-01-01
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a ``classical'' (macroscopic) signal resulting from the measurement of one bit (embodied in a two-state quantum system) is employed to determine the type of measurement carried out on the next bit, and so forth. In this way the two-bit gates in the Fourier transform can all be replaced by a smaller number of one-bit gates controlled by classical signals. Success in simplifying the Fourier transform suggests that it may be worthwhile looking for other ways of using semi-classical methods in quantum computing.
Efficient quantum computing with weak measurements
International Nuclear Information System (INIS)
Projective measurements with high quantum efficiency are often assumed to be required for efficient circuit-based quantum computing. We argue that this is not the case and show that the fact that they are not required was actually known previously but was 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 considering that the measurements used are of bounded weakness and some fixed but arbitrary probability of success less than unity is required. We also show that it is possible to perform the same computation with only local weak measurements, but this must necessarily introduce an exponential overhead.
The resource theory of stabilizer quantum computation
International Nuclear Information System (INIS)
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for fault-tolerant stabilizer computation. We introduce two quantitative measures—monotones—for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behavior. (paper)
Quantum computation over the butterfly network
Kinjo, Yoshiyuki; Soeda, Akihito; Turner, Peter S
2010-01-01
In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider performing a two qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource scenario introduced by Hayashi, which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that any controlled unitary operation can be performed without adding any entanglement resource. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.
Imperfect Detectors in Linear Optical Quantum Computers
Glancy, Scott; LoSecco, J. M.; Vasconcelos, H. M.; Tanner, C E
2002-01-01
We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency, there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gate...
Design Constraints for Nanometer Scale Quantum Computers
Mainieri, Ronnie
1994-01-01
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...
Dominant Strategies in Two Qubit Quantum Computations
Khan, Faisal Shah
2014-01-01
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented here for two qubit quantum computations that allows for the characterization of Nash equilibrium in these computations via the inner product of their state space. Nash equilibrium outcomes are optimal under given constraints and therefore o...
Statistical mechanics of classical and quantum computational complexity
Laumann, C. R.; Moessner, R.; A. Scardicchio; Sondhi, S. L.
2010-01-01
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 ...
Almost-classical quantum computers
Boes, Michiel; Vos, Alexis De; De Beule, Jan
2010-01-01
By means of a subgroup of the 2 X 2 unitary matrices, i.e. a subgroup Q of U(2), acting on a single qubit, we create a group X, acting on w qubits. If Q equals the group of order 2 consisting of the follower and the inverter, we recover S_{2^w}, i.e. the permutation matrices describing a classical reversible computer acting on w bits. If Q is another group of two 2 X 2 matrices, then a new kind of computing appears.
Computer animations of quantum field theory
International Nuclear Information System (INIS)
A visualization mehtod for quantum field theories based on the transfer matrix formalism is presented. It generates computer animations simulating the time evolution of complex physical systems subject to local Hamiltonians. The method may be used as a means of gaining insight to theories such as QCD, and as an educational tool in explaining high-energy physics. (orig.)
The quantum computer game: citizen science
Damgaard, Sidse; Mølmer, Klaus; Sherson, Jacob
2013-05-01
Progress in the field of quantum computation is hampered by daunting technical challenges. Here we present an alternative approach to solving these by enlisting the aid of computer players around the world. We have previously examined a quantum computation architecture involving ultracold atoms in optical lattices and strongly focused tweezers of light. In The Quantum Computer Game (see http://www.scienceathome.org/), we have encapsulated the time-dependent Schrödinger equation for the problem in a graphical user interface allowing for easy user input. Players can then search the parameter space with real-time graphical feedback in a game context with a global high-score that rewards short gate times and robustness to experimental errors. The game which is still in a demo version has so far been tried by several hundred players. Extensions of the approach to other models such as Gross-Pitaevskii and Bose-Hubbard are currently under development. The game has also been incorporated into science education at high-school and university level as an alternative method for teaching quantum mechanics. Initial quantitative evaluation results are very positive. AU Ideas Center for Community Driven Research, CODER.
Simulations of Probabilities for Quantum Computing
Zak, M.
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
Interactive Quantum Mechanics Quantum Experiments on the Computer
Brandt, S; Dahmen, H.D
2011-01-01
Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: • harmonic waves and wave packets, • free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), • two-particle systems, coupled harmonic oscillators, • distinguishable and indistinguishable particles, • coherent and squeezed states in time-dependent motion, • quantized angular momentum, • spin and magnetic resonance, • hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...
Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious
Cirasella, Jill
2009-01-01
This article is an annotated selection of the most important and informative Internet resources for learning about quantum computing, finding quantum computing literature, and tracking quantum computing news.
Quantum Computing: Theoretical versus Practical Possibility
Paraoanu, G S
2011-01-01
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle - there are no known laws of Nature that prevent it - yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I also introduce a distinction between "strong" and "weak" emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universal...
NMR spectra simulation for quantum computing
International Nuclear Information System (INIS)
Full text: Pulse NMR is one of the most serious candidates as an experimental technique for implementing quantum algorithms. To the present date, this technique is in fact the only one where full demonstrations of quantum algorithms implementations have been carried out, in spite of various technical difficulties. On NMR quantum computers, gates and subroutines are encoded as radiofrequency pulse sequences. A 'program output' is read directly on the measured spectra. On this work we simulate NMR spectra and show their evolution during algorithms implementations for two and three qubits systems. We will focus on Grover search, Quantum Fourier Transform, Shor factorization and Teleportation algorithms. Calculated spectra are compared to experimental data extracted from the literature. The main difficulties associated to the use of NMR to quantum computing, such as the exponential decrease of the signal upon increasing the number of qubits could, in principle, be partially removed by using ferromagnetic materials. However, broad NMR linewidths in these materials can mask logical operation. Some simulations are also presented to illustrate this point. (author)