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32
A functional quantum programming language
 In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are inte ..."
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Cited by 46 (12 self)
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This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms
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
"... ..."
Communicating quantum processes
 In POPL 2005
, 2005
"... We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the picalculus with primitives for measurement and transformation of quantum state; in particular, quantum ..."
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Cited by 39 (10 self)
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We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the picalculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems. 1
Quantum computation, categorical semantics and linear logic. quantph/0312174
, 2003
"... 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 ..."
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Cited by 27 (1 self)
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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
Structuring quantum effects: Superoperators as arrows
 Mathematical Structures in Computer Science, special issue on Quantum Programming Languages
, 2006
"... We show that quantum computation can be decomposed in a pure classical (functional) part and an effectful part modeling probabilities and measurement. The effectful part can be modeled using a generalization of monads called arrows. Both the functional and effectful parts can be elegantly expressed ..."
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Cited by 16 (8 self)
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We show that quantum computation can be decomposed in a pure classical (functional) part and an effectful part modeling probabilities and measurement. The effectful part can be modeled using a generalization of monads called arrows. Both the functional and effectful parts can be elegantly expressed in the Haskell programming language. 1
Between logic and quantic: a tract
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2003
"... We present a quantum interpretation of the perfect part of linear logic, by means of quantum coherent spaces. In particular this yields a novel interpretation of the reduction of the wave packet as the expression of ηconversion, a.k.a, extensionality. ..."
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Cited by 16 (1 self)
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We present a quantum interpretation of the perfect part of linear logic, by means of quantum coherent spaces. In particular this yields a novel interpretation of the reduction of the wave packet as the expression of ηconversion, a.k.a, extensionality.
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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Cited by 9 (5 self)
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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...”
Physics, Topology, Logic and Computation: A Rosetta Stone
, 2009
"... Category theory is a very general formalism, but there is a certain special way that physicists use categories which turns out to have close analogues in topology, logic and computation. A category has objects and morphisms, which represent things and ways to go between things. In physics, the objec ..."
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Cited by 5 (1 self)
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Category theory is a very general formalism, but there is a certain special way that physicists use categories which turns out to have close analogues in topology, logic and computation. A category has objects and morphisms, which represent things and ways to go between things. In physics, the objects are often physical systems, and the morphisms are processes turning a state of one physical system into a state of another system — perhaps
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.
Events, Causality and Symmetry
, 2008
"... The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences ..."
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Cited by 4 (2 self)
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The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.