Scrambling in quantum cellular automata

Scrambling is the delocalization of quantum information over a many-body system and underlies all quantumchaotic 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.

Automated summary

This article investigates the delocalization of quantum information in many-body systems and uses quantum cellular automata models for simulation. The study reveals that these models break ergodicity, showing quantum scarring. It is also found that the time scale of delocalization increases with the local Hilbert space dimension and follows a specific combinatorial pattern. Additionally, the study demonstrates that quantum scarring is mostly suppressed in semiclassical-chaotic systems, indicating their higher ergodicity.