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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 40 (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.
Structuring quantum effects: superoperators as arrows
 Mathematical. Structures in Comp. Sci
, 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
The Effects of
 Artificial Sources of Water on Rangeland Biodiversity. Environment Australia and CSIRO
, 1997
"... “Turing hoped that his abstractedpapertape model was so simple, so transparent and well defined, that it would not depend on any assumptions about physics that could conceivably be falsified, and therefore that it could become the basis of an abstract theory of computation that was independent of ..."
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“Turing hoped that his abstractedpapertape model was so simple, so transparent and well defined, that it would not depend on any assumptions about physics that could conceivably be falsified, and therefore that it could become the basis of an abstract theory of computation that was independent of the underlying physics. ‘He thought, ’ as Feynman once put it, ‘that he understood paper. ’ But he was mistaken. Real, quantummechanical paper is wildly different from the abstract stuff that the Turing machine uses. The Turing machine is entirely classical...”
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.
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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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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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.
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
Quantum data and control made easier
 Preliminary Proceedings of the 4th International Workshop on Quantum Programming Languages
, 2006
"... In this paper we define nQML, a functional quantum programming language that follows the “quantum data and control ” paradigm. In comparison to Altenkirch and Grattage’s QML, the control constructs of nQML are simpler and can implement quantum algorithms more directly and naturally. We avoid the unn ..."
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Cited by 5 (1 self)
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In this paper we define nQML, a functional quantum programming language that follows the “quantum data and control ” paradigm. In comparison to Altenkirch and Grattage’s QML, the control constructs of nQML are simpler and can implement quantum algorithms more directly and naturally. We avoid the unnecessary complexities of a linear type system by using types that carry the address of qubits in the quantum state. We provide a denotational semantics over density matrices and unitary transformations, inspired by Selinger’s semantics for QPL. Our semantics leads naturally to an interpreter for nQML, written in Haskell. We also explore the extension of nQML with polymorphic higherorder functions.