Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory

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dc.contributor.authorOspina, Juan
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupLógica y Computaciónspa
dc.creatorOspina, Juan
dc.date.accessioned2021-03-26T21:35:20Z
dc.date.available2021-03-26T21:35:20Z
dc.date.issued2015-05-21
dc.description.abstractThe recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called a "open-closed stringy topological quantum computera" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided. © 2015 SPIE.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=2248
dc.identifier.doi10.1117/12.2177363
dc.identifier.issn0277786X
dc.identifier.issn1996756X
dc.identifier.otherWOS;000357930800022
dc.identifier.otherSCOPUS;2-s2.0-84938704249
dc.identifier.urihttp://hdl.handle.net/10784/27414
dc.language.isoengeng
dc.publisherSPIE-INT SOC OPTICAL ENGINEERING
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84938704249&doi=10.1117%2f12.2177363&partnerID=40&md5=93e2c33c5211999c3563b05ab70053c8
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0277-786X
dc.sourceProceedings of SPIE
dc.subject.keywordAlgebraeng
dc.subject.keywordComputational linguisticseng
dc.subject.keywordFormal languageseng
dc.subject.keywordGeometryeng
dc.subject.keywordQuantum computerseng
dc.subject.keywordQuantum opticseng
dc.subject.keywordQuantum theoryeng
dc.subject.keywordSupersymmetryeng
dc.subject.keywordTheorem provingeng
dc.subject.keywordTopologyeng
dc.subject.keywordAutomated theorem provereng
dc.subject.keywordAutomated theorem provingeng
dc.subject.keywordHomotopieseng
dc.subject.keywordHomotopy typeseng
dc.subject.keywordLogical approacheseng
dc.subject.keywordMathematical designseng
dc.subject.keywordMonoidal categorieseng
dc.subject.keywordQuantum algorithmseng
dc.subject.keywordComputation theoryeng
dc.titleTopological and geometrical quantum computation in cohesive Khovanov homotopy type theoryeng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
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