Operator entanglement in local quantum circuits II: Solitons in chains of qubits

Bertini, Bruno (author), Kos, Pavel (author), Prosen, Tomaž (author)

We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits, allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly. Importantly, this does not bound the growth of complexity in chiral circuits, where solitons move only in one direction, say to the left. Indeed, in this case we observe numerically that operators on the odd sublattice have unbounded entanglement. Finally, we present a closed-form expression for the local-operator entanglement entropies in circuits with ultralocal solitons moving in both directions. Our results hold irrespectively of integrability.

• Language: English
• Keywords: entanglement, qubits, quantum many-body systems
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2020
• Number of pages: 23 str.
• Numbering: Vol. 8, art. no. 068
• PID: 20.500.12556/RUL-116060
• UDC: 530.145
• ISSN on article: 2542-4653
• DOI: 10.21468/SciPostPhys.8.4.068
• COBISS.SI-ID: 14722819
• Publication date in RUL: 12.05.2020

BERTINI, Bruno, KOS, Pavel and PROSEN, Tomaž, 2020, Operator entanglement in local quantum circuits II: Solitons in chains of qubits. SciPost physics [online]. 2020. Vol. 8, no. 068. [Accessed 11 April 2025]. DOI 10.21468/SciPostPhys.8.4.068. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=116060

Record is a part of a journal

• Title: SciPost physics
• Publisher: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

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.
• Licensing start date: 12.05.2020

Secondary language

• Language: Slovenian
• Keywords: kvantna prepletenost, kubiti, večdelčni sistemi

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

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