Scrambling in random unitary circuits: Exact results

Bruno Bertini and Lorenzo Piroli
Phys. Rev. B 102, 064305 – Published 10 August 2020

Abstract

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.

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  • Received 4 May 2020
  • Accepted 22 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.064305

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Bruno Bertini1 and Lorenzo Piroli2,3

  • 1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
  • 2Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
  • 3Munich Center for Quantum Science and Technology, Schellingstraße 4, 80799 München, Germany

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Issue

Vol. 102, Iss. 6 — 1 August 2020

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