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37
Dagger compact closed categories and completely positive maps (Extended Abstract)
 QPL 2005
, 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.
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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Cited by 10 (7 self)
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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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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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Cited by 7 (1 self)
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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.
Proof rules for the correctness of quantum programs
 Theoretical Computer Science
, 2007
"... We apply the notion of quantum predicate proposed by D’Hondt and Panangaden to analyze a simple language fragment which may describe the quantum part of a future quantum computer in Knill’s architecture. The notion of weakest liberal precondition semantics, introduced by Dijkstra for classical dete ..."
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Cited by 4 (2 self)
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We apply the notion of quantum predicate proposed by D’Hondt and Panangaden to analyze a simple language fragment which may describe the quantum part of a future quantum computer in Knill’s architecture. The notion of weakest liberal precondition semantics, introduced by Dijkstra for classical deterministic programs and by McIver and Morgan for probabilistic programs, is generalized to our quantum programs. To help reasoning about the correctness of quantum programs, we extend proof rules presented by Morgan for classical probabilistic loops to quantum loops. These rules are shown to be complete in the sense that any correct assertion about quantum loops can be proved using them. Some illustrative examples are also given to demonstrate the practicality of our proof rules. 1
Quantum Loop Programs ∗
, 2006
"... Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum ..."
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Cited by 3 (3 self)
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Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops. The computational process of a quantum loop is then described. Moreover, the notions of termination and almost termination are proposed for quantum loops. The function computed by a quantum loop is also defined. To illustrate these notions, we carefully examine two simplest classes of quantum loop programs: one qubit quantum loops, and two qubit quantum loops defined by controlled gates. In particular, we find a necessary and sufficient condition for termination of a general quantum loop on any mixed input state. A necessary and sufficient condition for almost termination on a pure input state is given too.
Reachability and termination analysis of concurrent quantum programs
 in: Proceedings of the 23rd International Conference on Concurrency Theory (CONCUR), Springer LNCS 7454, 2012
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