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Towards a quantum programming language
 Mathematical Structures in Computer Science
, 2004
"... The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of hardware circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data type ..."
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Cited by 169 (16 self)
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The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of hardware circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language. This language provides highlevel features such as loops, recursive procedures, and structured data types. It is statically typed, and it has an interesting denotational semantics in terms of complete partial orders of superoperators. 1
Synthesis of Reversible Logic Circuits
, 2003
"... Reversible or informationlossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minim ..."
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Cited by 87 (6 self)
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Reversible or informationlossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant inputoutput linepairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting the distribution of circuit sizes. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.
A lambda calculus for quantum computation
 SIAM Journal of Computing
"... The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propos ..."
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Cited by 71 (1 self)
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The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lambda calculus suitable for expressing and reasoning about quantum algorithms. In this paper we develop a quantum lambda calculus as an alternative model of quantum computation, which combines some of the benefits of both the quantum Turing machine and the quantum circuit models. The calculus turns out to be closely related to the linear lambda calculi used in the study of Linear Logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.
A lambda calculus for quantum computation with classical control
 IN PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON TYPED LAMBDA CALCULI AND APPLICATIONS (TLCA), VOLUME 3461 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
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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.
Reversible Logic Circuit Synthesis
 In International Conference on Computer Aided Design
, 2002
"... Reversible, or informationlossless, circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement for quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates ..."
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Cited by 42 (2 self)
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Reversible, or informationlossless, circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement for quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant inputoutput linepairs (temporary storage channels). We propose new constructions for reversible circuits composed of NOT, ControlledNOT, and TOFFOLI gates (the CNT gate library) based on permutation theory. A new algorithm is given to synthesize optimal reversible circuits using an arbitrary gate library, and we describe much faster heuristic algorithms. We also pursue applications of the proposed techniques to the synthesis of quantum circuits.
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 21 (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.
Toward a software architecture for quantum computing design tools
 Proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL
, 2004
"... Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quan ..."
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Cited by 21 (3 self)
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Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quantum computers have the potential to solve certain computational problems—for example, factoring composite numbers or comparing an unknown image against a large database— more efficiently than modern computers. They are also indispensable in controlling quantummechanical systems in emergent nanotechnology applications, such as secure optical communication, in which modern computers cannot natively operate on quantum data. Despite convincing laboratory demonstrations of
Quantum typing, in
 Proceedings of the 2nd International Workshop on Quantum Programming Languages
"... The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambdacalculus for the QRAM model, following the work of P. Selinger (2003) on quantum flowcharts. We define a callbyvalue operational semantics, and we develop a type system using aff ..."
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Cited by 19 (0 self)
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The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambdacalculus for the QRAM model, following the work of P. Selinger (2003) on quantum flowcharts. We define a callbyvalue operational semantics, and we develop a type system using affine intuitionistic linear logic. The main result of this preprint is the subjectreduction of the language.
A brief survey of quantum programming languages
 IN PROCEEDINGS OF THE 7TH INTERNATIONAL SYMPOSIUM ON FUNCTIONAL AND LOGIC PROGRAMMING
, 2004
"... This article is a brief and subjective survey of quantum programming language research. ..."
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Cited by 18 (0 self)
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This article is a brief and subjective survey of quantum programming language research.