Topological quantum computation of the Dold-Thom functor

Vista sencilla de ítem
dc.contributor.authorOspina, Juan
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupLógica y Computaciónspa
dc.creatorOspina, Juan
dc.date.accessioned2021-03-26T21:35:18Z
dc.date.available2021-03-26T21:35:18Z
dc.date.issued2014-05-22
dc.description.abstractA possible topological quantum computation of the Dold-Thom functor is presented. The method that will be used is the following: a) Certain 1+1-topological quantum field theories valued in symmetric bimonoidal categories are converted into stable homotopical data, using a machinery recently introduced by Elmendorf and Mandell; b) we exploit, in this framework, two recent results (independent of each other) on refinements of Khovanov homology: our refinement into a module over the connective k-theory spectrum and a stronger result by Lipshitz and Sarkar refining Khovanov homology into a stable homotopy type; c) starting from the Khovanov homotopy the Dold-Thom functor is constructed; d) the full construction is formulated as a topological quantum algorithm. It is conjectured that the Jones polynomial can be described as the analytical index of certain Dirac operator defined in the context of the Khovanov homotopy using the Dold-Thom functor. As a line for future research is interesting to study the corresponding supersymmetric model for which the Khovanov-Dirac operator plays the role of a supercharge. © 2014 SPIE.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1556
dc.identifier.doi10.1117/12.2050077
dc.identifier.issn0277786X
dc.identifier.issn1996756X
dc.identifier.otherWOS;000343113500020
dc.identifier.otherSCOPUS;2-s2.0-84906346523
dc.identifier.urihttp://hdl.handle.net/10784/27394
dc.language.isoengeng
dc.publisherSPIE-INT SOC OPTICAL ENGINEERING
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84906346523&doi=10.1117%2f12.2050077&partnerID=40&md5=91191b73a340c84fc362ceb4bc8bf469
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0277-786X
dc.sourceProceedings of SPIE
dc.subject.keywordMachineryeng
dc.subject.keywordQuantum computerseng
dc.subject.keywordQuantum opticseng
dc.subject.keywordQuantum theoryeng
dc.subject.keywordSupersymmetryeng
dc.subject.keywordDirac operatorseng
dc.subject.keywordFunctorseng
dc.subject.keywordHomotopieseng
dc.subject.keywordHomotopy typeseng
dc.subject.keywordJones polynomialeng
dc.subject.keywordQuantum algorithmseng
dc.subject.keywordQuantum field theoryeng
dc.subject.keywordSupersymmetric modelseng
dc.subject.keywordTopologyeng
dc.titleTopological quantum computation of the Dold-Thom functoreng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localDocumento de conferenciaspa

Archivos

Colecciones

Documentos de conferencia