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Communicating quantum processes
 In POPL 2005
, 2005
"... We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the picalculus with primitives for measurement and transformation of quantum state; in particular, quantum ..."
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Cited by 53 (14 self)
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We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the picalculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems. 1
Hidden translation and orbit coset in quantum computing
 IN PROC. 35TH ACM STOC
, 2003
"... We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of nonabelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently ..."
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Cited by 51 (10 self)
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We give efficient quantum algorithms for the problems of Hidden Translation and Hidden Subgroup in a large class of nonabelian solvable groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently Hidden Translation in Z n p, whenever p is a fixed prime. For the induction step, we introduce the problem Orbit Coset generalizing both Hidden Translation and Hidden Subgroup, and prove a powerful selfreducibility result: Orbit Coset in a finite group G is reducible to Orbit Coset in G/N and subgroups of N, for any solvable normal subgroup N of G. Our selfreducibility framework combined with Kuperberg’s subexponential quantum algorithm for solving Hidden Translation in any abelian group, leads to subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in any solvable group.
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 49 (3 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.
Introduction to Grassmann Manifolds and Quantum
 Computation, J. Applied Math
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Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... 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 ..."
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Cited by 36 (3 self)
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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 teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
Quantum walks: a comprehensive review
, 2012
"... Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting ..."
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Cited by 24 (0 self)
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Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete and continuoustime quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discretetime quantum walks. Furthermore, we have reviewed several algorithms based on both discrete and continuoustime quantum walks as well as a most important result: the computational universality of both continuous and discretetime quantum walks.
Modelling quantum computing in Haskell
 In Proceedings of the ACM SIGPLAN Workshop on Haskell
, 2003
"... The paper develops a model of quantum computing from the perspective of functional programming. The model explains the fundamental ideas of quantum computing at a level of abstraction that is familiar to functional programmers. The model also illustrates some of the inherent diculties in interpretin ..."
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Cited by 20 (1 self)
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The paper develops a model of quantum computing from the perspective of functional programming. The model explains the fundamental ideas of quantum computing at a level of abstraction that is familiar to functional programmers. The model also illustrates some of the inherent diculties in interpreting quantum mechanics and highlights the dierences between quantum computing and traditional (functional or otherwise) computing models.
Probabilistic model–checking of quantum protocols
 DCM 2006: PROCEEDINGS OF THE 2ND INTERNATIONAL WORKSHOP ON DEVELOPMENTS IN COMPUTATIONAL MODELS
, 2005
"... We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communicati ..."
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Cited by 17 (6 self)
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We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using presentday technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of prism, a probabilistic modelchecking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.
More on Optical Holonomic Quantum Computer
"... 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 ..."
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Cited by 14 (14 self)
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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 nonabelian Berry connections and curvatures explicitly in the special cases. Our main tool is unitary coherent operators based on Lie algebras su(n+1) and su(n,1), where the case of n = 1 is the previous one.