A functional quantum programming language
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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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2006
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| Online Access: | https://eprints.nottingham.ac.uk/10250/ |
| _version_ | 1848791053251903488 |
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| author | Grattage, Jonathan James |
| author_facet | Grattage, Jonathan James |
| author_sort | Grattage, Jonathan James |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:22:23Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-10250 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:22:23Z |
| publishDate | 2006 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-102502025-02-28T11:07:37Z https://eprints.nottingham.ac.uk/10250/ A functional quantum programming language Grattage, Jonathan James 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. 2006 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/10250/1/thesis.pdf Grattage, Jonathan James (2006) A functional quantum programming language. PhD thesis, University of Nottingham. 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. |
| spellingShingle | 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. Grattage, Jonathan James A functional quantum programming language |
| title | A functional quantum programming language |
| title_full | A functional quantum programming language |
| title_fullStr | A functional quantum programming language |
| title_full_unstemmed | A functional quantum programming language |
| title_short | A functional quantum programming language |
| title_sort | functional quantum programming language |
| topic | 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. |
| url | https://eprints.nottingham.ac.uk/10250/ |