Quantum algorithms for classical lattice models

We give efficient quantum algorithms to estimate the partition function of (i) the six-vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi-2D square lattice and (iv) the Z2 lattice gauge theory on a 3D s...

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Detalles Bibliográficos
Autores: Cuevas, Gemma de las, Dür, Wolfgang, Van den Nest, Maarten, Martin-Delgado, Miguel Ángel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:España
Institución:Universitat Pompeu Fabra
Repositorio:Repositorio Digital de la UPF
OAI Identifier:oai:repositori.upf.edu:10230/71752
Acceso en línea:http://hdl.handle.net/10230/71752
http://dx.doi.org/10.1088/1367-2630/13/9/093021
Access Level:acceso abierto
Palabra clave:Algorismes
Computació quàntica
Física
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spelling Quantum algorithms for classical lattice modelsCuevas, Gemma de lasDür, WolfgangVan den Nest, MaartenMartin-Delgado, Miguel ÁngelAlgorismesComputació quànticaFísicaWe give efficient quantum algorithms to estimate the partition function of (i) the six-vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi-2D square lattice and (iv) the Z2 lattice gauge theory on a 3D square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced by Van den Nest et al (2009 Phys. Rev. A 80 052334) and extended here.IOP Publishing202520252011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/71752http://dx.doi.org/10.1088/1367-2630/13/9/093021reponame:Repositorio Digital de la UPFinstname:Universitat Pompeu FabraInglésNew Journal of Physics. 2011 Sep 9;13(9):093021© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Published under a CC BY (Creative Commons Attribution) licence.http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositori.upf.edu:10230/717522026-06-12T07:21:37Z
dc.title.none.fl_str_mv Quantum algorithms for classical lattice models
title Quantum algorithms for classical lattice models
spellingShingle Quantum algorithms for classical lattice models
Cuevas, Gemma de las
Algorismes
Computació quàntica
Física
title_short Quantum algorithms for classical lattice models
title_full Quantum algorithms for classical lattice models
title_fullStr Quantum algorithms for classical lattice models
title_full_unstemmed Quantum algorithms for classical lattice models
title_sort Quantum algorithms for classical lattice models
dc.creator.none.fl_str_mv Cuevas, Gemma de las
Dür, Wolfgang
Van den Nest, Maarten
Martin-Delgado, Miguel Ángel
author Cuevas, Gemma de las
author_facet Cuevas, Gemma de las
Dür, Wolfgang
Van den Nest, Maarten
Martin-Delgado, Miguel Ángel
author_role author
author2 Dür, Wolfgang
Van den Nest, Maarten
Martin-Delgado, Miguel Ángel
author2_role author
author
author
dc.subject.none.fl_str_mv Algorismes
Computació quàntica
Física
topic Algorismes
Computació quàntica
Física
description We give efficient quantum algorithms to estimate the partition function of (i) the six-vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi-2D square lattice and (iv) the Z2 lattice gauge theory on a 3D square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced by Van den Nest et al (2009 Phys. Rev. A 80 052334) and extended here.
publishDate 2011
dc.date.none.fl_str_mv 2011
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/71752
http://dx.doi.org/10.1088/1367-2630/13/9/093021
url http://hdl.handle.net/10230/71752
http://dx.doi.org/10.1088/1367-2630/13/9/093021
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv New Journal of Physics. 2011 Sep 9;13(9):093021
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:Repositorio Digital de la UPF
instname:Universitat Pompeu Fabra
instname_str Universitat Pompeu Fabra
reponame_str Repositorio Digital de la UPF
collection Repositorio Digital de la UPF
repository.name.fl_str_mv
repository.mail.fl_str_mv
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