Scrambling in quantum cellular automata

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