Results 1  10
of
24
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 ..."
Abstract

Cited by 49 (3 self)
 Add to MetaCart
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 computation, categorical semantics and linear logic, available as arXiv:quantph/0312174
"... Abstract We develop a type theory and provide a denotational semantics for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic. In our semantics, variables inhabit certain Hilbert bundles, and computations are interpreted as the appropri ..."
Abstract

Cited by 33 (1 self)
 Add to MetaCart
(Show Context)
Abstract We develop a type theory and provide a denotational semantics for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic. In our semantics, variables inhabit certain Hilbert bundles, and computations are interpreted as the appropriate inner product preserving maps between Hilbert bundles. These bundles and maps form a symmetric monoidal closed category, as expected for a calculus based on linear logic.
An Algebra of Quantum Processes
"... We introduce an algebra qCCS of pure quantum processes in which communications by moving quantum states physically are allowed and computations are modeled by superoperators, but no classical data is explicitly involved. An operational semantics of qCCS is presented in terms of (nonprobabilistic) ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
(Show Context)
We introduce an algebra qCCS of pure quantum processes in which communications by moving quantum states physically are allowed and computations are modeled by superoperators, but no classical data is explicitly involved. An operational semantics of qCCS is presented in terms of (nonprobabilistic) labeled transition systems. Strong bisimulation between processes modeled in qCCS is defined, and its fundamental algebraic properties are established, including uniqueness of the solutions of recursive equations. To model sequential computation in qCCS, a reduction relation between processes is defined. By combining reduction relation and strong bisimulation we introduce the notion of strong reductionbisimulation, which is a device for observing interaction of computation and communication in quantum systems. Finally, a notion of strong approximate bisimulation (equivalently, strong bisimulation distance) and its reduction counterpart are introduced. It is proved that both approximate bisimilarity and approximate reductionbisimilarity are preserved by various constructors of quantum processes. This provides us with a formal tool for observing robustness of quantum processes against inaccuracy in the implementation of its
Probabilistic bisimilarities between quantum processes
, 2008
"... Modeling and analyzing concurrent quantum systems are very important both for distributed quantum computing and for quantum protocol verification. As a consequence, a general framework describing formally the communication and concurrency of complex quantum systems is necessary. We propose in this p ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Modeling and analyzing concurrent quantum systems are very important both for distributed quantum computing and for quantum protocol verification. As a consequence, a general framework describing formally the communication and concurrency of complex quantum systems is necessary. We propose in this paper a model qCCS for quantum concurrent systems, which is a natural quantum extension of classical valuepassing CCS with the input and output of quantum data, and unitary transformations and measurements on quantum systems. The operational semantics of qCCS is given based on probabilistic labeled transition systems. This semantics has many different features compared with the proposals in literature in order to describe input and output of quantum systems which are possibly correlated with other components. Based on this operational semantics, we introduce the notions of strong probabilistic bisimilarity and weak probabilistic bisimilarity between quantum processes and discuss some properties of them.
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 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
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
"... ar ..."
(Show Context)
An algebraic language for distributed quantum computing
 IEEE Transactions on Computers
"... Abstract—A classical circuit can be represented by a circuit graph or equivalently by a Boolean expression. The advantage of a circuit graph is that it can help us to obtain an intuitive understanding of the circuit under consideration, whereas the advantage of a Boolean expression is that it is sui ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract—A classical circuit can be represented by a circuit graph or equivalently by a Boolean expression. The advantage of a circuit graph is that it can help us to obtain an intuitive understanding of the circuit under consideration, whereas the advantage of a Boolean expression is that it is suited to various algebraic manipulations. In the literature, however, quantum circuits are mainly drawn as circuit graphs, and a formal language for quantum circuits that has a function similar to that of Boolean expressions for classical circuits is still missing. Certainly, quantum circuit graphs will become unmanageable when complicated quantum computing problems are encountered, and in particular when they have to be solved by employing the distributed paradigm where complex quantum communication networks are involved. In this paper, we design an algebraic language for formally specifying quantum circuits in distributed quantum computing. Using this language, quantum circuits can be represented in a convenient and compact way, similar to the way that we use Boolean expressions in dealing with classical circuits. Moreover, some fundamental algebraic laws for quantum circuits expressed in this language are established. These laws form a basis of rigorously reasoning about distributed quantum computing and quantum communication protocols. Index Terms—Quantum computing, circuits, distributed systems I.
Distributed Quantum Programming
, 2012
"... In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), an assembly language for distributed measurementbased quantum computations. We describe the formal language’s syntax and semantics, both operational and denotational, and state several properties ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), an assembly language for distributed measurementbased quantum computations. We describe the formal language’s syntax and semantics, both operational and denotational, and state several properties that are crucial to the practical usability of our language, such as equivalence of our semantics, as well as compositionality and contextfreeness of DMC programs. We show how to put these properties to use by constructing a composite program that implements distributed controlled operations, in the knowledge that the semantics of this program does not change under the various composition operations. Our formal model is the basis of a quantum virtual machine construction for distributed quantum computations, which we elaborate upon in the latter part of this work. This virtual machine embodies the formal semantics of DMC such that programming execution no longer needs to be analysed by hand. Far from a literal translation, it requires a substantial concretisation of the formal model at the level of data structures, naming conventions and abstraction mechanisms. At the same time we provide automatisation techniques for program specification where possible to obtain an expressive and userfriendly programming environment.
Open Bisimulation for Quantum Processes
"... Abstract. Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between q ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between quantum processes. We also give a modal characterisation of the behavioural equivalence, by extending the HennessyMilner logic to a quantum setting. 1