Caminhadas quânticas em tempo discreto em rede pequeno mundo
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFS |
Texto Completo: | http://ri.ufs.br/jspui/handle/riufs/15899 |
Resumo: | The quantum walks, besides being naturally used in the modeling of systems of this scale, has been widely used in the building quantum algorithms. In the last, both its formulation in continuous and discrete time, in some cases, presents better performance when compared to algorithms that use classical random walk. Among these formulations, the literature has highlighted the use of quantum walk in discrete time, in particular, its applicability in complex networks. The small world network is part of this type of structure. In this work, the discrete time quantum walk on this network is presented, analyzing the behavior of the probability distribution with the variation of the parameters q, which determines the topology of the network, and k, which defines the neighborhood closest to the vertex. A formalism is defined that describes this dynamic, allowing to numerically simulate the walk. The evolution of the probability distributions versus parameters reveals its tendency to spread, towards uniformity. Between this transition, there is a regime different from the characteristic ballistic behavior in a circular network. There is an attempt to determine a law of scale to describe this evolution, working only for a small range of parameters. |
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Ximenes, Jefferson JoséSouza, André Maurício Conceição de2022-06-20T18:36:08Z2022-06-20T18:36:08Z2020-02-28XIMENES, Jefferson José. Caminhadas quânticas em tempo discreto em rede pequeno mundo. 2020. 62 f. Dissertação (Mestrado em Física) - Universidade Federal de Sergipe, São Cristóvão, 2020.http://ri.ufs.br/jspui/handle/riufs/15899The quantum walks, besides being naturally used in the modeling of systems of this scale, has been widely used in the building quantum algorithms. In the last, both its formulation in continuous and discrete time, in some cases, presents better performance when compared to algorithms that use classical random walk. Among these formulations, the literature has highlighted the use of quantum walk in discrete time, in particular, its applicability in complex networks. The small world network is part of this type of structure. In this work, the discrete time quantum walk on this network is presented, analyzing the behavior of the probability distribution with the variation of the parameters q, which determines the topology of the network, and k, which defines the neighborhood closest to the vertex. A formalism is defined that describes this dynamic, allowing to numerically simulate the walk. The evolution of the probability distributions versus parameters reveals its tendency to spread, towards uniformity. Between this transition, there is a regime different from the characteristic ballistic behavior in a circular network. There is an attempt to determine a law of scale to describe this evolution, working only for a small range of parameters.O caminho aleatório quântico, além de ser naturalmente utilizado na modelagem de sistemas desta escala, tem sido amplamente empregado na construção de algorítimos quânticos. Neste último, tanto sua formulação em tempo contínuo quanto em discreto, em alguns casos apresentam melhor desempenho quando comparados a algoritmos que usam caminho aleatório clássico. Dentre essas formulações, a literatura tem dado destaque ao uso da caminhada quântica em tempo discreto, em especial, sua aplicabilidade em redes complexas. A rede pequeno mundo faz parte desse tipo de estrutura. Neste trabalho, é apresentado a caminhada quântica em tempo discreto sobre esta rede, analisando o comportamento da distribuição de probabilidade com a variação dos parâmetros q, que determina a topologia da rede, e k, que define a vizinhança mais próxima do vértice. É definido um formalismo que descreve esta dinâmica, permitindo simular numericamente a caminhada. A evolução das distribuições de probabilidade em função dos parâmetros revelam sua tendência de espalhamento, em direção a uniformidade. Entre essa transição, encontra-se um regime diferentemente do característico comportamento balístico em uma rede circular. Há uma tentativa de determinar uma lei de escala para descrever essa evolução, funcionando apenas para um pequeno intervalo dos parâmetros.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoporCaminhadas quânticasTempo discretoRede pequeno mundoQuantum walkerDiscrete timeSmall world networkCaminhadas quânticas em tempo discreto em rede pequeno mundoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPós-Graduação em FísicaUFSreponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessORIGINALJEFFERSON_JOSE_XIMENES.pdfJEFFERSON_JOSE_XIMENES.pdfapplication/pdf2888843https://ri.ufs.br/jspui/bitstream/riufs/15899/2/JEFFERSON_JOSE_XIMENES.pdf9447570e56c49a2460aff2b2eca92376MD52TEXTJEFFERSON_JOSE_XIMENES.pdf.txtJEFFERSON_JOSE_XIMENES.pdf.txtExtracted texttext/plain71983https://ri.ufs.br/jspui/bitstream/riufs/15899/3/JEFFERSON_JOSE_XIMENES.pdf.txta0529f156890ca2929e12e0ba64056f5MD53THUMBNAILJEFFERSON_JOSE_XIMENES.pdf.jpgJEFFERSON_JOSE_XIMENES.pdf.jpgGenerated Thumbnailimage/jpeg1136https://ri.ufs.br/jspui/bitstream/riufs/15899/4/JEFFERSON_JOSE_XIMENES.pdf.jpg7cd8dab273f3a211d27755c464cec188MD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/15899/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51riufs/158992022-06-20 15:36:08.534oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2022-06-20T18:36:08Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false |
dc.title.pt_BR.fl_str_mv |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
title |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
spellingShingle |
Caminhadas quânticas em tempo discreto em rede pequeno mundo Ximenes, Jefferson José Caminhadas quânticas Tempo discreto Rede pequeno mundo Quantum walker Discrete time Small world network |
title_short |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
title_full |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
title_fullStr |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
title_full_unstemmed |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
title_sort |
Caminhadas quânticas em tempo discreto em rede pequeno mundo |
author |
Ximenes, Jefferson José |
author_facet |
Ximenes, Jefferson José |
author_role |
author |
dc.contributor.author.fl_str_mv |
Ximenes, Jefferson José |
dc.contributor.advisor1.fl_str_mv |
Souza, André Maurício Conceição de |
contributor_str_mv |
Souza, André Maurício Conceição de |
dc.subject.por.fl_str_mv |
Caminhadas quânticas Tempo discreto Rede pequeno mundo |
topic |
Caminhadas quânticas Tempo discreto Rede pequeno mundo Quantum walker Discrete time Small world network |
dc.subject.eng.fl_str_mv |
Quantum walker Discrete time Small world network |
description |
The quantum walks, besides being naturally used in the modeling of systems of this scale, has been widely used in the building quantum algorithms. In the last, both its formulation in continuous and discrete time, in some cases, presents better performance when compared to algorithms that use classical random walk. Among these formulations, the literature has highlighted the use of quantum walk in discrete time, in particular, its applicability in complex networks. The small world network is part of this type of structure. In this work, the discrete time quantum walk on this network is presented, analyzing the behavior of the probability distribution with the variation of the parameters q, which determines the topology of the network, and k, which defines the neighborhood closest to the vertex. A formalism is defined that describes this dynamic, allowing to numerically simulate the walk. The evolution of the probability distributions versus parameters reveals its tendency to spread, towards uniformity. Between this transition, there is a regime different from the characteristic ballistic behavior in a circular network. There is an attempt to determine a law of scale to describe this evolution, working only for a small range of parameters. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-02-28 |
dc.date.accessioned.fl_str_mv |
2022-06-20T18:36:08Z |
dc.date.available.fl_str_mv |
2022-06-20T18:36:08Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
XIMENES, Jefferson José. Caminhadas quânticas em tempo discreto em rede pequeno mundo. 2020. 62 f. Dissertação (Mestrado em Física) - Universidade Federal de Sergipe, São Cristóvão, 2020. |
dc.identifier.uri.fl_str_mv |
http://ri.ufs.br/jspui/handle/riufs/15899 |
identifier_str_mv |
XIMENES, Jefferson José. Caminhadas quânticas em tempo discreto em rede pequeno mundo. 2020. 62 f. Dissertação (Mestrado em Física) - Universidade Federal de Sergipe, São Cristóvão, 2020. |
url |
http://ri.ufs.br/jspui/handle/riufs/15899 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.program.fl_str_mv |
Pós-Graduação em Física |
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UFS |
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