Scrambling in random unitary circuits: exact results
ID Bertini, Bruno (Author), ID Piroli, Lorenzo (Author)

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We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged Rényi-2 tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a “maximally chaotic” subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is based on a standard mapping onto an averaged folded tensor network, that can be studied by means of appropriate recurrence relations. By means of the same method, we also revisit the computation of out-of-time-ordered correlation functions, rederiving known formulas for Haar-random unitary circuits, and presenting an exact result for maximally chaotic random dual-unitary gates.

Keywords:nonequilibrium statistical mechanics, quantum chaos
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Author Accepted Manuscript
Number of pages:Str. 064305-1-064305-25
Numbering:Vol. 102, iss. 6
PID:20.500.12556/RUL-124028 This link opens in a new window
ISSN on article:2469-9950
DOI:10.1103/PhysRevB.102.064305 This link opens in a new window
COBISS.SI-ID:43003139 This link opens in a new window
Publication date in RUL:21.12.2020
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Record is a part of a journal

Title:Physical review
Publisher:American Physical Society
COBISS.SI-ID:2997348 This link opens in a new window

Secondary language

Keywords:neravnovesna statistična mehanika, kvantni kaos


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

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

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