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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 110 (13 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
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 49 (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.
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 47 (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 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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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 26 (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 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 17 (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
"... Abstract. This article is a brief and subjective survey of quantum programming language research. 1 Quantum Computation Quantum computing is a relatively young subject. It has its beginnings in 1982, when Paul Benioff and Richard Feynman independently pointed out that a quantum mechanical system can ..."
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Cited by 11 (0 self)
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Abstract. This article is a brief and subjective survey of quantum programming language research. 1 Quantum Computation Quantum computing is a relatively young subject. It has its beginnings in 1982, when Paul Benioff and Richard Feynman independently pointed out that a quantum mechanical system can be used to perform computations [11, p.12]. Feynman’s interest in quantum computation was motivated by the fact that it is computationally very expensive to simulate quantum physical systems on classical computers. This is due to the fact that such simulation involves the manipulation is extremely large matrices (whose dimension is exponential in the size of the quantum system being simulated). Feynman conceived of quantum computers as a means of simulating nature much more efficiently. The evidence to this day is that quantum computers can indeed perform certain tasks more efficiently than classical computers. Perhaps the bestknown example is Shor’s factoring algorithm, by which a quantum computer can find
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 11 (1 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 Programming
, 2004
"... The subject of this work is quantum programming — the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, ..."
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Cited by 5 (4 self)
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The subject of this work is quantum programming — the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, a recent generalisation of the wellestablished predicative programming. It supports the style of program development in which each programming step is proven correct as it is made. We inherit the advantages of the theory, such as its generality, simple treatment of recursive programs, and time and space complexity. Our theory of quantum programming provides tools to write both classical and quantum specifications, develop quantum programs that implement these specifications, and reason about their comparative time and space complexity all in the same framework.
Quantum Programming Languages: An Introductory Overview
, 2006
"... The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area ..."
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Cited by 4 (0 self)
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The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area. Then, several of the approaches are described in more detail. The article concludes with a brief survey of current research activities and a tabular summary of a selection of QPLs, which have been published so far.