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On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorZÉMOR, Gilles
dc.date.accessioned2024-04-04T02:38:17Z
dc.date.available2024-04-04T02:38:17Z
dc.date.created2009-05
dc.date.issued2009-06
dc.date.conference2009-06-01
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190863
dc.description.abstractEnWe review constructions of quantum surface codes and give an alternative, algebraic, construction of the known classes of surface codes that have fixed rate and growing minimum distance. This construction borrows from Margulis's family of Cayley graphs with large girths, and highlights the analogy between quantum surface codes and cycle codes of graphs in the classical case. We also attempt a brief foray into the class of quantum topological codes arising from higher dimensional manifolds and find these examples to have the same constraint on the rate and minimum distance as in the 2-dimensional case.
dc.description.sponsorshipCOdes Correcteurs Quantiques - ANR-08-EMER-0003
dc.language.isoen
dc.publisherSpringer
dc.source.titleCoding and Cryptology, second international workshop IWCC 2009
dc.title.enOn Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction
dc.typeCommunication dans un congrès
dc.subject.halMathématiques [math]/Théorie de l'information et codage [math.IT]
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
bordeaux.page259-273
bordeaux.volume5557
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleInternational Workshop on Coding and Cryptology
bordeaux.countryCN
bordeaux.title.proceedingCoding and Cryptology, second international workshop IWCC 2009
bordeaux.conference.cityZhangjiajie
bordeaux.peerReviewedoui
hal.identifierhal-00387084
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2009-06-05
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00387084v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Coding%20and%20Cryptology,%20second%20international%20workshop%20IWCC%202009&rft.date=2009-06&rft.volume=5557&rft.spage=259-273&rft.epage=259-273&rft.au=Z%C3%89MOR,%20Gilles&rft.genre=unknown


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