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arXiv · 2301.07722

Scrambling in quantum cellular automata

Brian Kent·Sarah Racz·Sanjit Shashi
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Abstract

Scrambling is the delocalization of quantum information over a many-body system and underlies all quantum-chaotic dynamics. We employ discrete quantum cellular automata as classically simulable toy models of scrambling. We observe that these automata break ergodicity, i.e. they exhibit quantum scarring. We also find that the time-scale of scrambling rises with the local Hilbert-space dimension and obeys a specific combinatorial pattern. We then show that scarring is mostly suppressed in a semiclassical limit, demonstrating that semiclassical-chaotic systems are more ergodic.

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Brian Kent, Sarah Racz, Sanjit Shashi. 2023-01-18. Scrambling in quantum cellular automata. https://doi.org/10.1103/physrevb.107.144306

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