Classical control and quantum circuits in enriched category theory
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language,...
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| Format: | Conference item |
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Elsevier
2018
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| _version_ | 1797078981327978496 |
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| author | Rennela, M Staton, S |
| author_facet | Rennela, M Staton, S |
| author_sort | Rennela, M |
| collection | OXFORD |
| description | We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types. |
| first_indexed | 2024-03-07T00:39:07Z |
| format | Conference item |
| id | oxford-uuid:82705340-fda0-450f-96a0-f92b1440d46b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:39:07Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:82705340-fda0-450f-96a0-f92b1440d46b2022-03-26T21:37:23ZClassical control and quantum circuits in enriched category theoryConference itemhttp://purl.org/coar/resource_type/c_5794uuid:82705340-fda0-450f-96a0-f92b1440d46bSymplectic Elements at OxfordElsevier2018Rennela, MStaton, SWe describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types. |
| spellingShingle | Rennela, M Staton, S Classical control and quantum circuits in enriched category theory |
| title | Classical control and quantum circuits in enriched category theory |
| title_full | Classical control and quantum circuits in enriched category theory |
| title_fullStr | Classical control and quantum circuits in enriched category theory |
| title_full_unstemmed | Classical control and quantum circuits in enriched category theory |
| title_short | Classical control and quantum circuits in enriched category theory |
| title_sort | classical control and quantum circuits in enriched category theory |
| work_keys_str_mv | AT rennelam classicalcontrolandquantumcircuitsinenrichedcategorytheory AT statons classicalcontrolandquantumcircuitsinenrichedcategorytheory |