Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom

Bensa, Jaš (author), Žnidarič, Marko (author)

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.

• Language: English
• Keywords: statistical physics, quantum physics, quantum information, quantum entanglement, quantum gates, quantum phase transitions, quantum quench, general physics, condensed matter, materials, applied physics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 28 str.
• Numbering: Vol. 11, iss. 3, art. 031019
• PID: 20.500.12556/RUL-144712
• UDC: 536.9
• ISSN on article: 2160-3308
• DOI: 10.1103/PhysRevX.11.031019
• COBISS.SI-ID: 72645891
• Publication date in RUL: 09.03.2023

BENSA, Jaš and ŽNIDARIČ, Marko, 2021, Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom. Physical review [online]. 2021. Vol. 11, no. 3,  031019. [Accessed 11 April 2025]. DOI 10.1103/PhysRevX.11.031019. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=144712

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., X
• Publisher: American Physical Society
• ISSN: 2160-3308
• COBISS.SI-ID: 19686152

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: statistična fizika, kvantna fizika

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: J1-1698
• Name: Načrtovanje večdelčnega transporta

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika