Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom

We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process, and we prove that there are large spectral equivalence clas...

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Autores principales:	Jaš Bensa, Marko Žnidarič
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/ffd490300d514707a87f80ef8f6fd719
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spelling	oai:doaj.org-article:ffd490300d514707a87f80ef8f6fd7192021-12-02T18:36:02ZFastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom10.1103/PhysRevX.11.0310192160-3308https://doaj.org/article/ffd490300d514707a87f80ef8f6fd7192021-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031019http://doi.org/10.1103/PhysRevX.11.031019https://doaj.org/toc/2160-3308We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process, and we prove that there are large spectral equivalence classes—different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This result is caused by expansion coefficients that grow exponentially with system size, resulting in a “phantom” eigenvalue and is due to nonorthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon also occurs in random circuits with nonoptimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance in other non-Hermitian settings, including correlations.Jaš BensaMarko ŽnidaričAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031019 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Jaš Bensa Marko Žnidarič Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
description	We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process, and we prove that there are large spectral equivalence classes—different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This result is caused by expansion coefficients that grow exponentially with system size, resulting in a “phantom” eigenvalue and is due to nonorthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon also occurs in random circuits with nonoptimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance in other non-Hermitian settings, including correlations.
format	article
author	Jaš Bensa Marko Žnidarič
author_facet	Jaš Bensa Marko Žnidarič
author_sort	Jaš Bensa
title	Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
title_short	Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
title_full	Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
title_fullStr	Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
title_full_unstemmed	Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom
title_sort	fastest local entanglement scrambler, multistage thermalization, and a non-hermitian phantom
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/ffd490300d514707a87f80ef8f6fd719
work_keys_str_mv	AT jasbensa fastestlocalentanglementscramblermultistagethermalizationandanonhermitianphantom AT markoznidaric fastestlocalentanglementscramblermultistagethermalizationandanonhermitianphantom
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Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom

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