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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
Monads Need Not Be Endofunctors
"... Abstract. We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finitedimensional vector spaces, untyped and typed λcalculus syntax and indexed containers. We show that the Kleisli and EilenbergMoore constr ..."
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Cited by 9 (0 self)
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Abstract. We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finitedimensional vector spaces, untyped and typed λcalculus syntax and indexed containers. We show that the Kleisli and EilenbergMoore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between monads and relative monads. Arrows are also an instance of relative monads. 1
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 4 (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.
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.
Quantum Circuits: From a Network to a OneWay Model
"... We present elements of quantum circuits translations from the standard network (or circuit) model to the oneway one. We present a general translation scheme, give an account of currently existing tools to apply the scheme, and propose an extension of those tools into a complete translation calculus ..."
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We present elements of quantum circuits translations from the standard network (or circuit) model to the oneway one. We present a general translation scheme, give an account of currently existing tools to apply the scheme, and propose an extension of those tools into a complete translation calculus. We analyze the set of difficulties incurred from such work, and show an engendered opening to new sets of discussions and ideas. Among others, this paper extends the findings to the notions of graphical concatenation, graph state reduction (GSR) and graph state extension (GSE) passes. Further, it proposes an algorithm for running the (extended) measurement calculus with acceptable efficiency. 1.
QPL 2006 From reversible to irreversible computations
"... In this paper we study the relation between reversible and irreversible computation applicable to different models of computation — here we are considering classical and quantum computation. We develop an equational theory of reversible computations and an associated theory of irreversible computati ..."
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In this paper we study the relation between reversible and irreversible computation applicable to different models of computation — here we are considering classical and quantum computation. We develop an equational theory of reversible computations and an associated theory of irreversible computations which is obtained by marking some inputs as preinitialised heap and some outputs as garbage to be thrown away at the end of the computation. We present three laws which apply to irreversible classical and quantum computations and show that von Neumann’s measurement postulate is derivable from them. We discuss the question whether these laws are complete for irreversible quantum computations. Key words: Reversible computation, irreversible computation, quantum computation, categorical models. 1