{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T03:05:42Z","timestamp":1767927942403,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T00:00:00Z","timestamp":1662508800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Modern quantum programming languages integrate quantum resources and\nclassical control. They must, on the one hand, be linearly typed to reflect the\nno-cloning property of quantum resources. On the other hand, high-level and\npractical languages should also support quantum circuits as first-class\ncitizens, as well as families of circuits that are indexed by some classical\nparameters. Quantum programming languages thus need linear dependent type\ntheory. This paper defines a general semantic structure for such a type theory\nvia certain fibrations of monoidal categories. The categorical model of the\nquantum circuit description language Proto-Quipper-M by Rios and Selinger\n(2017) constitutes an example of such a fibration, which means that the\nlanguage can readily be integrated with dependent types. We then devise both a\ngeneral linear dependent type system and a dependently typed extension of\nProto-Quipper-M, and provide them with operational semantics as well as a\nprototype implementation.<\/jats:p>","DOI":"10.46298\/lmcs-18(3:28)2022","type":"journal-article","created":{"date-parts":[[2022,9,7]],"date-time":"2022-09-07T13:27:02Z","timestamp":1662557222000},"source":"Crossref","is-referenced-by-count":4,"title":["Linear Dependent Type Theory for Quantum Programming Languages"],"prefix":"10.46298","volume":"Volume 18, Issue 3","author":[{"given":"Peng","family":"Fu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kohei","family":"Kishida","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Selinger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,9,7]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/10009\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/10009\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:18:29Z","timestamp":1687292309000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/6930"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,7]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(3:28)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2004.13472v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2004.13472v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2004.13472v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2004.13472","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2004.13472","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,7]]},"article-number":"6930"}}