Principle of majorization: Application to random quantum circuits

Autores
Vallejos, Raúl O.; De Melo, Fernando; Carlo, Gabriel Gustavo
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We test the principle of majorization [J. I. Latorre and M. A. Martín-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates → ∞) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated to asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and non-universal classes of random quantum circuits, and they also detect the complexity of some non-universal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as a indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators (OTOCs).
Fil: Vallejos, Raúl O.. Centro Brasileiro de Pesquisas Físicas; Brasil
Fil: De Melo, Fernando. Centro Brasileiro de Pesquisas Físicas; Brasil
Fil: Carlo, Gabriel Gustavo. Comisión Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones No Nucleares. Gerencia Física (CAC). Departamento de Física de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Majorization
Quantum computation
Quantum complexity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/153485
Acceder
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spelling Principle of majorization: Application to random quantum circuitsVallejos, Raúl O.De Melo, FernandoCarlo, Gabriel GustavoMajorizationQuantum computationQuantum complexityhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We test the principle of majorization [J. I. Latorre and M. A. Martín-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates → ∞) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated to asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and non-universal classes of random quantum circuits, and they also detect the complexity of some non-universal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as a indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators (OTOCs).Fil: Vallejos, Raúl O.. Centro Brasileiro de Pesquisas Físicas; BrasilFil: De Melo, Fernando. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Carlo, Gabriel Gustavo. Comisión Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones No Nucleares. Gerencia Física (CAC). Departamento de Física de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Physical Society2021-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/153485Vallejos, Raúl O.; De Melo, Fernando; Carlo, Gabriel Gustavo; Principle of majorization: Application to random quantum circuits; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 104; 1; 7-2021; 1-82469-99262469-9934CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.104.012602info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2102.09999info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:31Zoai:ri.conicet.gov.ar:11336/153485instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:48:31.975CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Principle of majorization: Application to random quantum circuits
title Principle of majorization: Application to random quantum circuits
spellingShingle Principle of majorization: Application to random quantum circuits
Vallejos, Raúl O.
Majorization
Quantum computation
Quantum complexity
title_short Principle of majorization: Application to random quantum circuits
title_full Principle of majorization: Application to random quantum circuits
title_fullStr Principle of majorization: Application to random quantum circuits
title_full_unstemmed Principle of majorization: Application to random quantum circuits
title_sort Principle of majorization: Application to random quantum circuits
dc.creator.none.fl_str_mv Vallejos, Raúl O.
De Melo, Fernando
Carlo, Gabriel Gustavo
author Vallejos, Raúl O.
author_facet Vallejos, Raúl O.
De Melo, Fernando
Carlo, Gabriel Gustavo
author_role author
author2 De Melo, Fernando
Carlo, Gabriel Gustavo
author2_role author
author
dc.subject.none.fl_str_mv Majorization
Quantum computation
Quantum complexity
topic Majorization
Quantum computation
Quantum complexity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We test the principle of majorization [J. I. Latorre and M. A. Martín-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates → ∞) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated to asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and non-universal classes of random quantum circuits, and they also detect the complexity of some non-universal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as a indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators (OTOCs).
Fil: Vallejos, Raúl O.. Centro Brasileiro de Pesquisas Físicas; Brasil
Fil: De Melo, Fernando. Centro Brasileiro de Pesquisas Físicas; Brasil
Fil: Carlo, Gabriel Gustavo. Comisión Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones No Nucleares. Gerencia Física (CAC). Departamento de Física de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We test the principle of majorization [J. I. Latorre and M. A. Martín-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates → ∞) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated to asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and non-universal classes of random quantum circuits, and they also detect the complexity of some non-universal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as a indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators (OTOCs).
publishDate 2021
dc.date.none.fl_str_mv 2021-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/153485
Vallejos, Raúl O.; De Melo, Fernando; Carlo, Gabriel Gustavo; Principle of majorization: Application to random quantum circuits; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 104; 1; 7-2021; 1-8
2469-9926
2469-9934
CONICET Digital
CONICET
url http://hdl.handle.net/11336/153485
identifier_str_mv Vallejos, Raúl O.; De Melo, Fernando; Carlo, Gabriel Gustavo; Principle of majorization: Application to random quantum circuits; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 104; 1; 7-2021; 1-8
2469-9926
2469-9934
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.104.012602
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2102.09999
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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