Caminhada quântica escalonada em grade hexagonal

• Autor(a) principal: Chagas, Bruno de Oliveira
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/294
• topic: Computação quântica; Caminhada quântica escalonada; Grade hexagonal; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::METODOLOGIA E TECNICAS DA COMPUTACAO::PROCESSAMENTO GRAFICO (GRAPHICS)

Quantum computing presents itself as one of the most promising areas in the search for algorithms for classical problems, making it possible to broaden the computing frontiers on theoretical aspects. Quantum computing suggests a variety of quantum walk models which have already been successfully used in classical computing as random walks and randomized algorithms achieving solutions for several problems such as: element distinction, matrix multiplication verification, associativity of binary operation, triangle finding problem, testing group commutativity and searching problems. Throughout this thesis we shall use the staggered quantum walk model with hamiltonians that generalizes other quantum walk models. The first problem we analyzed was the clique lattice where we found its spectral decomposition and a similar behavior was observed regarding the coined quantum walk on two-dimensional lattice. Finally, we took up the problem of a hexagonal lattice, a very interesting graph which is comparable to the graphene structure with several applications. We applied a general decomposition to the operator, using staggered quantum walk with hamiltonians, found out the non-existence of localization phenomena and we also verify its performance – the best, up to now – on searching problems.