Possible universal quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant

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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.accessioned2021-03-26T21:35:18Z
dc.date.available2021-03-26T21:35:18Z
dc.date.issued2012-01-01
dc.description.abstractPossible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such algorithms are resulting from adaptations of the recently proposed Kauffmans` algorithm for the standard Khovanov homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs-Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the hardware for the implementation of the proposed quantum algorithms. © 2012 SPIE.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1576
dc.identifier.doi10.1117/12.918886
dc.identifier.issn0277786X
dc.identifier.issn1996756X
dc.identifier.otherWOS;000305737400021
dc.identifier.otherSCOPUS;2-s2.0-84863978328
dc.identifier.urihttp://hdl.handle.net/10784/27395
dc.language.isoengeng
dc.publisherSPIE-INT SOC OPTICAL ENGINEERING
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84863978328&doi=10.1117%2f12.918886&partnerID=40&md5=981d9899ad12a69bd62b24e0970dbfdf
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0277-786X
dc.sourceProceedings of SPIE
dc.subject.keywordAtiyah-Singer theoremeng
dc.subject.keywordGauge theoryeng
dc.subject.keywordGeneralized Khovanov homologyeng
dc.subject.keywordHomotopieseng
dc.subject.keywordKhovanov homologyeng
dc.subject.keywordQuantum invariantseng
dc.subject.keywordRasmussen's invarianteng
dc.subject.keywordAlgorithmseng
dc.subject.keywordPolynomialseng
dc.subject.keywordQuantum computerseng
dc.subject.keywordQuantum opticseng
dc.subject.keywordTopologyeng
dc.subject.keywordQuantum theoryeng
dc.titlePossible universal quantum algorithms for generalized Khovanov homology and the Rasmussen's invarianteng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
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