Quantum algorithms for virtual Jones polynomials via thistlethwaite theorems

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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.issued2010-01-01
dc.description.abstractRecently a quantum algorithm for the Jones polynomial of virtual links was proposed by Kauffman and Dye via the implementation of the virtual braid group in anyonic topological quantum computation when the virtual crossings are considered as generalized swap gates. Also recently, a mathematical method for the computation of the Jones polynomial of a given virtual link in terms of the relative Tuttle polynomial of its face (Tait) graph with some suitable variable substitutions was proposed by Diao and Hetyei. The method of Diao and Hetyei is offered as an alternative to the ribbon graph approach according to which the Tutte polynomial of a given virtual link is computed in terms of the Bollobás- Riordan polynomial of the corresponding ribbon graph. The method of Diao and Hetyei can be considered as an extension of the celebrated Thistlethwaite theorem according to which invariant polynomials for knots and links are derived from invariant polynomials for graphs. Starting from these ideas we propose a quantum algorithm for the Jones polynomial of a given virtual link in terms of the generalized Tutte polynomials by exploiting the Thistlethwaite theorem and the Kauffman algorithm. Our method is claimed as the quantum version of the Diao-Hetyei method. Possible supersymmetric implementations of our algortihm are discussed jointly with its formulations using topological quantum lambda calculus. © 2010 SPIE.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1608
dc.identifier.doi10.1117/12.849776
dc.identifier.issn0277786X
dc.identifier.issn1996756X
dc.identifier.otherWOS;000285050700005
dc.identifier.otherSCOPUS;2-s2.0-77953819161
dc.identifier.urihttp://hdl.handle.net/10784/27398
dc.language.isoengeng
dc.publisherSPIE-INT SOC OPTICAL ENGINEERING
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-77953819161&doi=10.1117%2f12.849776&partnerID=40&md5=f5af32f2c01124a8ffee0758f1db7185
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0277-786X
dc.sourceProceedings of SPIE
dc.subject.keywordAS index theoremeng
dc.subject.keywordHadamardeng
dc.subject.keywordIndex theoremeng
dc.subject.keywordJones polynomialeng
dc.subject.keywordQuantum computationeng
dc.subject.keywordSupersymmetrieseng
dc.subject.keywordVirtual Linkeng
dc.subject.keywordAlgorithmseng
dc.subject.keywordComputational linguisticseng
dc.subject.keywordDifferentiation (calculus)eng
dc.subject.keywordQuantum computerseng
dc.subject.keywordQuantum opticseng
dc.subject.keywordQuantum theoryeng
dc.subject.keywordTopologyeng
dc.subject.keywordPolynomialseng
dc.titleQuantum algorithms for virtual Jones polynomials via thistlethwaite theoremseng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
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