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On the construction of new toric quantum codes and quantum burst-error-correcting codes

dc.contributor.authorTrinca, Cibele Cristina
dc.contributor.authorInterlando, J. Carmelo
dc.contributor.authorPalazzo, Reginaldo
dc.contributor.authorde Andrade, Antonio Aparecido [UNESP]
dc.contributor.authorWatanabe, Ricardo Augusto
dc.contributor.institutionFederal University of Tocantins
dc.contributor.institutionSan Diego State University
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.date.accessioned2023-07-29T13:15:20Z
dc.date.available2023-07-29T13:15:20Z
dc.date.issued2023-05-01
dc.description.abstractA toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is provided by constructing a classical cyclic code on the square lattice Zq× Zq for all odd integers q≥ 5 and, consequently, new toric quantum codes are constructed on such square lattices and from geometrically uniform codes regardless of whether q can be represented as a sum of two squares. Furthermore, this work supplies for each q the polyomino shapes that tessellate the corresponding square lattices and, consequently, tile the lattice Z2 . The quantum channel without memory to be considered for these constructed toric quantum codes is symmetric, since the Z2 -lattice is autodual. Moreover, we propose a quantum interleaving technique by using the constructed toric quantum codes, which shows that the code rate and the coding gain of the interleaved toric quantum codes are better than the code rate and the coding gain of Kitaev’s toric quantum codes for q= 2 n+ 1 , where n≥ 2 , and of an infinite class of Bombin and Martin-Delgado’s toric quantum codes. In addition to the proposed quantum interleaving technique that improves such parameters, it can be used for burst-error correction in errors which are located, quantum data stored and quantum channels with memory.en
dc.description.affiliationDepartment of Biotechnology and Bioprocess Engineering Federal University of Tocantins, TO
dc.description.affiliationDepartment of Mathematics and Statistics San Diego State University
dc.description.affiliationSchool of Electrical and Computer Engineering Campinas State University, SP
dc.description.affiliationDepartment of Mathematics São Paulo State University, SP
dc.description.affiliationSchool of Mathematics Statistics and Scientific Computing Campinas State University, SP
dc.description.affiliationUnespDepartment of Mathematics São Paulo State University, SP
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipIdCNPq: 101862/2022-9
dc.identifierhttp://dx.doi.org/10.1007/s11128-023-03931-4
dc.identifier.citationQuantum Information Processing, v. 22, n. 5, 2023.
dc.identifier.doi10.1007/s11128-023-03931-4
dc.identifier.issn1573-1332
dc.identifier.issn1570-0755
dc.identifier.scopus2-s2.0-85159859991
dc.identifier.urihttp://hdl.handle.net/11449/247409
dc.language.isoeng
dc.relation.ispartofQuantum Information Processing
dc.sourceScopus
dc.subjectQuantum Burst-Error Correction
dc.subjectQuantum Interleaving
dc.subjectSquare Lattice
dc.subjectToric Quantum Code
dc.titleOn the construction of new toric quantum codes and quantum burst-error-correcting codesen
dc.typeArtigo
dspace.entity.typePublication
unesp.author.orcid0000-0003-2857-7410[1]
unesp.author.orcid0000-0003-4928-043X[2]
unesp.author.orcid0000-0002-3219-8061[3]
unesp.author.orcid0000-0001-6452-2236[4]
unesp.author.orcid0000-0001-7957-4805[5]

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