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594
Efficient simulation of quantum systems by quantum computers
, 1998
"... We show that the time evolution of the wave function of a quantummechanical manyparticle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a per ..."
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Cited by 79 (0 self)
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We show that the time evolution of the wave function of a quantummechanical manyparticle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a performance which can’t be expected from any classical simulation of a quantum system. We then show how quantities 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 computers.
Quantum communication
, 1995
"... 1 First, I would like to thank my advisor Noam Nisan. During the two years I have been working with Noam, he has been a most costructive in uence on me, teaching me how to think and write in a clear way. Iwould also liketothankmymyfellow students, who during this time had to su er hearing me lecturi ..."
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Cited by 72 (0 self)
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1 First, I would like to thank my advisor Noam Nisan. During the two years I have been working with Noam, he has been a most costructive in uence on me, teaching me how to think and write in a clear way. Iwould also liketothankmymyfellow students, who during this time had to su er hearing me lecturing my ideas � this goes especially to Amnon Tashma who hasn't recovered yet. My parents deserve a special thank, not only for getting me up to this point, but also for the help they have given me with the di cult task of writing this thesis in English. Finally I would like tothankmy wife Ruthie for working around my short \mental going to work &quot; periods, unlike the others she will have tocontinue living with me. 2
A functional quantum programming language
 In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are inte ..."
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Cited by 70 (12 self)
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This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms
Quantum Algorithm For Hilberts Tenth Problem
 Int.J.Theor.Phys
, 2003
"... We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert’s tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomp ..."
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Cited by 59 (10 self)
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We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert’s tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle—that is, if certain hamiltonian and its ground state can be physically constructed according to the proposal—quantum computability would surpass classical computability as delimited by the ChurchTuring thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles. 1
QuantumInspired Computing
, 1995
"... The paper identifies and demonstrates the feasibility of a novel computational paradigm which is inspired by the principles of quantum mechanics and quantum computing. A brief history of quantum computing and basic exposition of quantum mechanics are provided, followed by a detailed description of S ..."
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Cited by 58 (9 self)
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The paper identifies and demonstrates the feasibility of a novel computational paradigm which is inspired by the principles of quantum mechanics and quantum computing. A brief history of quantum computing and basic exposition of quantum mechanics are provided, followed by a detailed description of Shor's quantum `algorithm' for factoring very large numbers. An extension to Shor's method is described, and this leads to two further applications of `quantuminspired' methods: sorting, and the 15puzzle. In all cases, quantuminspired methods require the use of `classical' methods to determine whether the candidate answers provided by the quantuminspired methods are correct. Finally, some basic methodological principles and guidelines are provided for quantuminspired computing. The aim is not to provide a formal exposition of quantuminspired computing but to identify its novelty and potential use in tackling NPhard problems. 1 Introduction It has been estimated that every two years ...
Parallel quantum computation
 Complexity, Entropy, and the Physics of Information,SFI Studies in the Sciences of Complexity
, 1990
"... A computer is a physical system which has a very general ability to simulate other physical systems (and in particular, other computers). In this paper we investigate the question of whether microscopic quantum systems can be computers. Using a reversible cellular automaton model of computation we i ..."
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Cited by 54 (10 self)
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A computer is a physical system which has a very general ability to simulate other physical systems (and in particular, other computers). In this paper we investigate the question of whether microscopic quantum systems can be computers. Using a reversible cellular automaton model of computation we illustrate several approaches to this question. We then attempt to extend Feynman’s construction of a quantum computer in order to arrive at a quantum model of parallel processing. 1
Implementation of a quantum search algorithm on a quantum computer
 Nature
, 1998
"... The simulation of quantum mechanical systems with classical computers appears to be a computationally intractable problem. In 1982 Feynman 1 reversed this observation, suggesting that quantum mechanical systems have an information processing capability much greater than that of corresponding classic ..."
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Cited by 53 (4 self)
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The simulation of quantum mechanical systems with classical computers appears to be a computationally intractable problem. In 1982 Feynman 1 reversed this observation, suggesting that quantum mechanical systems have an information processing capability much greater than that of corresponding classical systems, and thus could be used to implement a new type of powerful computer. In 1985 Deutsch 2 described a quantum mechanical Turing machine, showing that quantum computers could indeed be constructed. Since then there has been extensive research in this field, but while the theory is fairly well understood actually building a quantum computer has proved extremely difficult, and only two methods have been used to demonstrate quantum logic gates: ion traps, 3,4 and nuclear magnetic resonance (NMR). 5,6 NMR quantum computers have previously been used to demonstrate quantum algorithms to solve the two bit Deutsch problem. 7,8 Here we show how such a computer can be used to implement a fast quantum
Nonabelian anyons and topological quantum computation
 Reviews of Modern Physics
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Cited by 52 (0 self)
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
Quantum Programming Languages  Survey and Bibliography
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2006
"... The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechan ..."
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Cited by 47 (2 self)
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The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechanics, and the design of compilers for quantum programming languages. This article justifies the study of quantum programming languages, presents the basics of quantum computing, surveys the literature in quantum programming languages, and indicates directions for future research.
The Power of Vacillation in Language Learning
, 1992
"... Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there ..."
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Cited by 46 (13 self)
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Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are classes of languages that can be learned if convergence in the limit to up to (n+1) exactly correct grammars is allowed but which cannot be learned if convergence in the limit is to no more than n grammars, where the no more than n grammars can each make finitely many mistakes. This contrasts sharply with results of Barzdin and Podnieks and, later, Case and Smith, for learnability from both positive and negative data. A subset principle from a 1980 paper of Angluin is extended to the vacillatory and other criteria of this paper. This principle, provides a necessary condition for circumventing overgeneralization in learning from positive data. It is applied to prove another theorem to the eff...