Scrambling via braiding of nonabelions

Zhi-Cheng Yang, Konstantinos Meichanetzidis, Stefanos Kourtis, and Claudio Chamon
Phys. Rev. B 99, 045132 – Published 18 January 2019

Abstract

We study how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of entanglement spectrum statistics. In particular, we focus on the degree of scrambling, defined as the randomness produced by braiding, at the same amount of entanglement entropy. To quantify the degree of randomness, we define a distance between the entanglement spectrum level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence DKL. We study DKL numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. For comparison, we also obtain DKL for the Sachdev-Ye-Kitaev model of Majorana fermions with all-to-all interactions, random unitary circuits built out of (a) Hadamard (H), π/8 (T), and CNOT gates, and (b) random unitary circuits built out of two-qubit Haar random unitaries. To compare the degree of randomness that different systems produce beyond entanglement entropy, we look at DKL as a function of the Page limit-normalized entanglement entropy S/Smax. Our results reveal a hierarchy of scrambling among various models—even for the same amount of entanglement entropy—at intermediate times, whereas all models exhibit the same late-time behavior. In particular, we find that braiding of Fibonacci anyons randomizes initial product states more efficiently than the universal H+T+CNOT set.

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  • Received 11 April 2018

DOI:https://doi.org/10.1103/PhysRevB.99.045132

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhi-Cheng Yang1, Konstantinos Meichanetzidis2, Stefanos Kourtis1, and Claudio Chamon1

  • 1Physics Department, Boston University, Boston, Massachusetts 02215, USA
  • 2School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom

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Issue

Vol. 99, Iss. 4 — 15 January 2019

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