Scrambling via Braiding of Nonabelions
Zhi-Cheng Yang, Konstantinos Meichanetzidis, Stefanos Kourtis, and, Claudio Chamon

TL;DR
This paper investigates how braiding non-Abelian anyons, like Fibonacci anyons, scrambles quantum information by analyzing entanglement spectrum statistics and comparing it to other models, revealing a hierarchy of scrambling efficiency.
Contribution
It introduces a novel measure using Kullback-Leibler divergence to quantify the degree of quantum state scrambling via braiding in non-Abelian anyons, comparing it with other models.
Findings
Fibonacci anyons scramble more efficiently than H+T+CNOT circuits.
All models converge to similar late-time behavior despite different intermediate scrambling.
Hierarchy of scrambling efficiency is observed at intermediate times.
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 . We study numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. For comparison, we also obtain for the Sachdev-Ye-Kitaev model of Majorana fermions with all-to-all interactions, random unitary circuits built out of (a) Hadamard (H), (T), and…
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