On the construction of new toric quantum codes and quantum burst-error-correcting codes
dc.contributor.author | Trinca, Cibele Cristina | |
dc.contributor.author | Interlando, J. Carmelo | |
dc.contributor.author | Palazzo, Reginaldo | |
dc.contributor.author | de Andrade, Antonio Aparecido [UNESP] | |
dc.contributor.author | Watanabe, Ricardo Augusto | |
dc.contributor.institution | Federal University of Tocantins | |
dc.contributor.institution | San Diego State University | |
dc.contributor.institution | Universidade Estadual de Campinas (UNICAMP) | |
dc.contributor.institution | Universidade Estadual Paulista (UNESP) | |
dc.date.accessioned | 2023-07-29T13:15:20Z | |
dc.date.available | 2023-07-29T13:15:20Z | |
dc.date.issued | 2023-05-01 | |
dc.description.abstract | A 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.affiliation | Department of Biotechnology and Bioprocess Engineering Federal University of Tocantins, TO | |
dc.description.affiliation | Department of Mathematics and Statistics San Diego State University | |
dc.description.affiliation | School of Electrical and Computer Engineering Campinas State University, SP | |
dc.description.affiliation | Department of Mathematics São Paulo State University, SP | |
dc.description.affiliation | School of Mathematics Statistics and Scientific Computing Campinas State University, SP | |
dc.description.affiliationUnesp | Department of Mathematics São Paulo State University, SP | |
dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
dc.description.sponsorshipId | CNPq: 101862/2022-9 | |
dc.identifier | http://dx.doi.org/10.1007/s11128-023-03931-4 | |
dc.identifier.citation | Quantum Information Processing, v. 22, n. 5, 2023. | |
dc.identifier.doi | 10.1007/s11128-023-03931-4 | |
dc.identifier.issn | 1573-1332 | |
dc.identifier.issn | 1570-0755 | |
dc.identifier.scopus | 2-s2.0-85159859991 | |
dc.identifier.uri | http://hdl.handle.net/11449/247409 | |
dc.language.iso | eng | |
dc.relation.ispartof | Quantum Information Processing | |
dc.source | Scopus | |
dc.subject | Quantum Burst-Error Correction | |
dc.subject | Quantum Interleaving | |
dc.subject | Square Lattice | |
dc.subject | Toric Quantum Code | |
dc.title | On the construction of new toric quantum codes and quantum burst-error-correcting codes | en |
dc.type | Artigo | |
dspace.entity.type | Publication | |
unesp.author.orcid | 0000-0003-2857-7410[1] | |
unesp.author.orcid | 0000-0003-4928-043X[2] | |
unesp.author.orcid | 0000-0002-3219-8061[3] | |
unesp.author.orcid | 0000-0001-6452-2236[4] | |
unesp.author.orcid | 0000-0001-7957-4805[5] |