Scrambling in quantum cellular automata

TL;DR

This paper uses quantum cellular automata to model quantum scrambling, revealing ergodicity breaking through quantum scarring and how scrambling time scales with local Hilbert space dimension, with implications for semiclassical limits.

Contribution

It introduces quantum cellular automata as toy models for scrambling, demonstrating ergodicity breaking and the impact of semiclassical limits on quantum chaos.

Findings

Quantum cellular automata exhibit quantum scarring.

Scrambling time scales with local Hilbert-space dimension.

Scarring is suppressed in the semiclassical limit.

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.