Possible universal quantum algorithms for generalized Turaev-Viro invariants

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dc.contributor.authorVelez, Mario
dc.contributor.authorOspina, Juan
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupLógica y Computaciónspa
dc.creatorVelez, Mario
dc.creatorOspina, Juan
dc.date.accessioned2021-03-26T21:35:19Z
dc.date.available2021-03-26T21:35:19Z
dc.date.issued2011-01-01
dc.description.abstractAn emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for graphs (Tutte polynomial and Bollobás-Riordan polynomial); topological invariants for 3-manifolds (Reshetiskin-Turaev, Turaev-Viro and Turaer-Viro-Ocneanu invariants) and topological invariants for 4-manifolds (Crane-Yetter invariants). In a few words, TQC is concerned with the formulation of quantum algorithms for the computation of these topological invariants in quantum topology. Given that one of the fundamental achievements of quantum topology was the discovery of strong connections between monoidal categories and 3-dimensional manifolds, in TQC is possible and necessary to exploit such connections with the purpose to formulate universal quantum algorithms for topological invariants of 3-manifolds. In the present work we make an exploration of such possibilities. Specifically we search for universal quantum algorithms for generalized Turaev-Viro invariants of 3-manifolds such as the Turaev-Viro-Ocneanu invariants, the Kashaev-Baseilhac-Benedetti invariants of 3-manifolds with links and the Geer-Kashaev-Turaev invariants of 3-manifolds with a link and a principal bundle. We also look for physical systems (three dimensional topological insulators and three-dimensional gravity) over which implement the resulting universal topological quantum algorithms.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1594
dc.identifier.doi10.1117/12.883617
dc.identifier.issn0277786X
dc.identifier.issn1996756X
dc.identifier.otherWOS;000292734600026
dc.identifier.otherSCOPUS;2-s2.0-79960404070
dc.identifier.urihttp://hdl.handle.net/10784/27397
dc.language.isoengeng
dc.publisherSPIE-INT SOC OPTICAL ENGINEERING
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-79960404070&doi=10.1117%2f12.883617&partnerID=40&md5=96e8769204c10f40afbd313b790aa92b
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0277-786X
dc.sourceProceedings of SPIE
dc.subject.keywordGeneralized Turaev-Viro invariantseng
dc.subject.keywordJones polynomialeng
dc.subject.keywordQuantum gravityeng
dc.subject.keywordQuantum topologyeng
dc.subject.keywordSpherical categorieseng
dc.subject.keywordTopological insulatorseng
dc.subject.keywordWRT invariantseng
dc.subject.keywordAlgorithmseng
dc.subject.keywordComputational linguisticseng
dc.subject.keywordElectric insulatorseng
dc.subject.keywordPolynomialseng
dc.subject.keywordQuantum computerseng
dc.subject.keywordQuantum opticseng
dc.subject.keywordQuantum theoryeng
dc.subject.keywordThree dimensionaleng
dc.subject.keywordTopologyeng
dc.titlePossible universal quantum algorithms for generalized Turaev-Viro invariantseng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localDocumento de conferenciaspa

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