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Scrambling via braiding of nonabelions

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [3]
  1. Boston Univ., MA (United States); DOE/OSTI
  2. Univ. of Leeds (United Kingdom)
  3. Boston Univ., MA (United States)
+ Show Author Affiliations
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. Furthermore, 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.
Research Organization:
Boston Univ., MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
FG02-06ER46316
OSTI ID:
1609748
Alternate ID(s):
OSTI ID: 1491287
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 4 Vol. 99; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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