Construction of topological quantum codes on bidimensional manifolds / Analise e construção de codigos quanticos topologicos sobre variedades bidimensionais
AUTOR(ES)
Clarice Dias de Albuquerque
DATA DE PUBLICAÇÃO
2009
RESUMO
In this work we present an extensive study of topological quantum codes. As a consequence, new promising ideas, concepts and results are also presented. First of all, new toric quantum codes are constructed among which the [[d2,2,d]] class stands out as the best known so far. This proposed construction of toric codes is realized based upon group theory and combinatorial analysis. Regarding the topological quantum codes in surfaces with genus g = 2, we consider a construction method based on hyperbolic geometry and so generalizing Kitaev s construction. We reproduce and enlarge the class of quantum codes with distance 3 as a consequence of the embedding of complete graphs in surface with specific genus. This class was first proposed by Bombin andMartin-Delgado. The latter class is geometrically described and its parameters are explicitly exhibited. We also obtain a class of MDS (Maximum Distance Separable) codes in surfaces with genus g = 2,3,4 and 5, obtained by the proposed construction are tabulated and analyzed
ASSUNTO(S)
teoria da codificação lattice theory geometria hiperbolica coding theory hyperbolic geometry teoria dos reticulados
