Algebraic and Geometric Methods for Construction of Topological Quantum Codes from Lattices

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.contributorUTFPR Univ Tecn Fed Parana-
Autor(es): dc.contributorInst Fed Parana Campus Pitanga-
Autor(es): dc.contributorUniversidade Estadual de Maringá (UEM)-
Autor(es): dc.creatorCarvalho, Edson Donizete de-
Autor(es): dc.creatorSoares Jr, Waldir Silva-
Autor(es): dc.creatorCopatti, Douglas Fernando-
Autor(es): dc.creatorMartins, Carlos Alexandre Ribeiro-
Autor(es): dc.creatorSilva, Eduardo Brandani da-
Data de aceite: dc.date.accessioned2025-08-21T21:54:29Z-
Data de disponibilização: dc.date.available2025-08-21T21:54:29Z-
Data de envio: dc.date.issued2025-04-29-
Data de envio: dc.date.issued2024-10-01-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.3390/axioms13100676-
Fonte completa do material: dc.identifierhttps://hdl.handle.net/11449/302909-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/302909-
Descrição: dc.descriptionCurrent work provides an algebraic and geometric technique for building topological quantum codes. From the lattice partition derived of quotient lattices Lambda '/Lambda of index m combined with geometric technique of the projections of vector basis Lambda ' over vector basis Lambda, we reproduce surface codes found in the literature with parameter [[2m,2,|a|+|b|]] for the case Lambda=Z2 and m=a2+b2, where a and b are integers that are not null, simultaneously. We also obtain a new class of surface code with parameters [[2m,2,|a|+|b|]] from the Lambda=A2-lattice when m can be expressed as m=a2+ab+b2, where a and b are integer values. Finally, we will show how this technique can be extended to the construction of color codes with parameters [[18m,4,6(|a|+|b|)]] by considering honeycomb lattices partition A2/Lambda ' of index m=9(a2+ab+b2) where a and b are not null integers.-
Descrição: dc.descriptionUNESP Univ Estadual Paulista, Dept Math, BR-15385000 Ilha Solteira, Brazil-
Descrição: dc.descriptionUTFPR Univ Tecn Fed Parana, Dept Math, BR-85503390 Pato Branco, Brazil-
Descrição: dc.descriptionInst Fed Parana Campus Pitanga, Dept Math, BR-85200000 Pitanga, Brazil-
Descrição: dc.descriptionUEM Univ Estadual Maringa, Dept Math, Ave Colombo 5790, BR-87020900 Maringa, Brazil-
Descrição: dc.descriptionUNESP Univ Estadual Paulista, Dept Math, BR-15385000 Ilha Solteira, Brazil-
Formato: dc.format16-
Idioma: dc.languageen-
Publicador: dc.publisherMdpi-
Relação: dc.relationAxioms-
???dc.source???: dc.sourceWeb of Science-
Palavras-chave: dc.subjectsurface codes-
Palavras-chave: dc.subjectcolor codes-
Palavras-chave: dc.subjectflat torus-
Palavras-chave: dc.subjectlattice-
Título: dc.titleAlgebraic and Geometric Methods for Construction of Topological Quantum Codes from Lattices-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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