Quantum walk on the generalized birkhoff polytope graph
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.3390/e23101239 http://hdl.handle.net/11449/229615 |
Resumo: | We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ɛ), where ɛ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m1.5 /ɛ). |
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Repositório Institucional da UNESP |
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Quantum walk on the generalized birkhoff polytope graphCountingGeneralized Birkhoff polytopeQuantum walkSamplingTransportation problemWe study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ɛ), where ɛ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m1.5 /ɛ).Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ)Department of Industrial Manufacturing & Systems Engineering Texas Tech UniversityCampus of Itapeva Universidade Estadual Paulista (Unesp)National Laboratory of Scientific Computing (LNCC)Campus of Itapeva Universidade Estadual Paulista (Unesp)CNPq: 302203/2021-4CNPq: 308923/2019-7FAPERJ: CNE E-26/202.872/2018Texas Tech UniversityUniversidade Estadual Paulista (UNESP)National Laboratory of Scientific Computing (LNCC)Cação, RafaelCortez, Lucasde Farias, IsmaelKozyreff, Ernee [UNESP]Moqadam, Jalil KhatibiPortugal, Renato2022-04-29T08:34:50Z2022-04-29T08:34:50Z2021-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.3390/e23101239Entropy, v. 23, n. 10, 2021.1099-4300http://hdl.handle.net/11449/22961510.3390/e231012392-s2.0-85115999389Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengEntropyinfo:eu-repo/semantics/openAccess2022-04-29T08:34:50Zoai:repositorio.unesp.br:11449/229615Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:56:09.541514Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Quantum walk on the generalized birkhoff polytope graph |
title |
Quantum walk on the generalized birkhoff polytope graph |
spellingShingle |
Quantum walk on the generalized birkhoff polytope graph Cação, Rafael Counting Generalized Birkhoff polytope Quantum walk Sampling Transportation problem |
title_short |
Quantum walk on the generalized birkhoff polytope graph |
title_full |
Quantum walk on the generalized birkhoff polytope graph |
title_fullStr |
Quantum walk on the generalized birkhoff polytope graph |
title_full_unstemmed |
Quantum walk on the generalized birkhoff polytope graph |
title_sort |
Quantum walk on the generalized birkhoff polytope graph |
author |
Cação, Rafael |
author_facet |
Cação, Rafael Cortez, Lucas de Farias, Ismael Kozyreff, Ernee [UNESP] Moqadam, Jalil Khatibi Portugal, Renato |
author_role |
author |
author2 |
Cortez, Lucas de Farias, Ismael Kozyreff, Ernee [UNESP] Moqadam, Jalil Khatibi Portugal, Renato |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Texas Tech University Universidade Estadual Paulista (UNESP) National Laboratory of Scientific Computing (LNCC) |
dc.contributor.author.fl_str_mv |
Cação, Rafael Cortez, Lucas de Farias, Ismael Kozyreff, Ernee [UNESP] Moqadam, Jalil Khatibi Portugal, Renato |
dc.subject.por.fl_str_mv |
Counting Generalized Birkhoff polytope Quantum walk Sampling Transportation problem |
topic |
Counting Generalized Birkhoff polytope Quantum walk Sampling Transportation problem |
description |
We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ɛ), where ɛ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m1.5 /ɛ). |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-10-01 2022-04-29T08:34:50Z 2022-04-29T08:34:50Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.3390/e23101239 Entropy, v. 23, n. 10, 2021. 1099-4300 http://hdl.handle.net/11449/229615 10.3390/e23101239 2-s2.0-85115999389 |
url |
http://dx.doi.org/10.3390/e23101239 http://hdl.handle.net/11449/229615 |
identifier_str_mv |
Entropy, v. 23, n. 10, 2021. 1099-4300 10.3390/e23101239 2-s2.0-85115999389 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Entropy |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128584419639296 |