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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 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.
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.
Structuring quantum effects: Superoperators as arrows
 Mathematical Structures in Computer Science, special issue on Quantum Programming Languages
, 2006
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Reversing algebraic process calculi
 in: FOSSACS’06, LNCS 3921 (2006
, 2006
"... Abstract. Reversible computation has a growing number of promising application areas such as the modelling of biochemical systems, program debugging and testing, and even programming languages for quantum computing. We formulate a procedure for converting operators of standard algebraic process calc ..."
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Abstract. Reversible computation has a growing number of promising application areas such as the modelling of biochemical systems, program debugging and testing, and even programming languages for quantum computing. We formulate a procedure for converting operators of standard algebraic process calculi such as CCS, ACP and CSP into reversible operators, while preserving their operational semantics. 1
Hoare Logic for Quantum Programs ∗
, 2009
"... Hoare logic is a foundation of axiomatic semantics of classical programs and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to build a logical foundation of programming methodology for qua ..."
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Hoare logic is a foundation of axiomatic semantics of classical programs and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to build a logical foundation of programming methodology for quantum computers, we develop a fullfledged Hoare logic for both partial and total correctness of quantum programs. It is proved that this logic is (relatively) complete by exploiting the power of weakest preconditions and weakest liberal preconditions for quantum programs.
1 Quantum Lambda Calculus
"... We discuss the design of a typed lambda calculus for quantum computation. After a brief discussion of the role of higherorder functions in quantum information theory, we define the quantum lambda calculus and its operational semantics. Safety invariants, such as the nocloning property, are enforce ..."
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We discuss the design of a typed lambda calculus for quantum computation. After a brief discussion of the role of higherorder functions in quantum information theory, we define the quantum lambda calculus and its operational semantics. Safety invariants, such as the nocloning property, are enforced by a static type system that is based on intuitionistic linear logic. We also describe a type inference algorithm, and a categorical semantics. 1.1
Towards modelchecking quantum security protocols
 PROCEEDINGS OF THE FIRST WORKSHOP ON QUANTUM SECURITY: QSEC’07
, 2007
"... Logics for reasoning about quantum states have been given in the literature. In this paper, we extend one such logic with temporal constructs mimicking the standard computational tree logic used to reason about classical transition systems. We investigate the modelchecking problem for this temporal ..."
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Cited by 7 (2 self)
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Logics for reasoning about quantum states have been given in the literature. In this paper, we extend one such logic with temporal constructs mimicking the standard computational tree logic used to reason about classical transition systems. We investigate the modelchecking problem for this temporal quantum logic and illustrate its use by reasoning about the BB84 key distribution protocol.
Quantum computation tree logic – model checking and complete calculus
 International Journal of Quantum Information
"... Logics for reasoning about quantum states and their evolution have been given in the literature. In this paper we consider Quantum Computation Tree Logic (QCTL), which adds temporal modalities to exogenous quantum propositional logic. We give a sound and complete axiomatization of QCTL and combine t ..."
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Logics for reasoning about quantum states and their evolution have been given in the literature. In this paper we consider Quantum Computation Tree Logic (QCTL), which adds temporal modalities to exogenous quantum propositional logic. We give a sound and complete axiomatization of QCTL and combine the standard CTL modelchecking algorithm with the dEQPL modelchecking algorithm to obtain a modelchecking algorithm for QCTL. Finally we illustrate the use of the logic by reasoning about the BB84 key distribution protocol.
QML: Quantum data and control
, 2005
"... We introduce the language QML, a functional language for quantum computations on finite types. QML introduces quantum data and control structures, and integrates reversible and irreversible quantum computation. QML is based on strict linear logic, hence weakenings, which may lead to decoherence, hav ..."
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Cited by 6 (1 self)
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We introduce the language QML, a functional language for quantum computations on finite types. QML introduces quantum data and control structures, and integrates reversible and irreversible quantum computation. QML is based on strict linear logic, hence weakenings, which may lead to decoherence, have to be explicit. We present an operational semantics of QML programs using quantum circuits, and a denotational semantics using superoperators.
The Quantum IO Monad
"... The Quantum IO monad is a purely functional interface to quantum programming implemented as a Haskell library. At the same time it provides a constructive semantics of quantum programming. The QIO monad separates reversible (i.e. unitary) and irreversible (i.e. probabilistic) computations and provid ..."
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Cited by 5 (2 self)
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The Quantum IO monad is a purely functional interface to quantum programming implemented as a Haskell library. At the same time it provides a constructive semantics of quantum programming. The QIO monad separates reversible (i.e. unitary) and irreversible (i.e. probabilistic) computations and provides a reversible let operation (ulet), allowing us to use ancillas (auxiliary qubits) in a modular fashion. QIO programs can be simulated either by calculating a probability distribution or by embedding it into the IO monad using the random number generator. As an example we present a complete implementation of Shor’s algorithm.