A functional quantum programming language

Grattage, Jonathan James (2006) A functional quantum programming language. PhD thesis, University of Nottingham.

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Abstract

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 into superoperators, via the operational semantics, made precise by the category Q. Extensional equality for QML programs is also presented, via a mapping from FQC morphisms into the category Q.

Item Type:Thesis (PhD)
Supervisors:Altenkirch, Thorsten
Belavkin, Viacheslav
Uncontrolled Keywords:QML, quantum programming, quantum programming language, functional programming, quantum functional programming, quantum circuits, quantum circuit model, QPL, FQC, FCC, FxC, Finite Quantum Computation, Finite Classical Computation, Finite Computation, reversible quantum computation, reversible classical computation, reversible computation, category theory, denotational semantics, operational semantics, linear algebra, Haskell, functional programming, superoperators, super-operators, super operators, irreversible quantum computation, irreversible classical computation, irreversible computation, categorical semantics, Deutsch Algorith, Shor's Algorithm, Quantum Teleportation, quantum Fourier transform, quantum data, quantum control, syntax and typing rules.
Faculties/Schools:UK Campuses > Faculty of Science > School of Computer Science
UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:250
Deposited By:Jonathan James Grattage
Deposited On:20 Mar 2008
Last Modified:06 Feb 2009 14:43

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