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Quantum walks with quantum chaotic coins: Loschmidt echo, classical limit, and thermalization
Omanakuttan S.,
Published in Cornell University Press
2021
PMID: 33601574
Volume: 103
   
Issue: 1
Abstract
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo-like fidelity plays a central role, and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-body localization and coupled kicked rotors, and saturates to a value that depends on the relative coin and walker space dimensions. In a coin-dominated scenario, the chaos can thermalize the quantum walk to typical random states such that the entanglement saturates at the Haar averaged Page value, unlike in a walker-dominated case when atypical states seem to be produced. © 2021 American Physical Society.
About the journal
JournalPhysical Review E
PublisherCornell University Press
ISSN24700045
Open AccessNo