Chaos and thermalization in Clifford-Floquet dynamics

TL;DR

This paper investigates how Clifford Quantum Cellular Automata (QCA) under Floquet dynamics lead to thermalization in qubit systems, highlighting conditions for ergodicity and the distinction between weak and strong thermalization.

Contribution

It demonstrates that many initial states, including short-range entangled states, thermalize under Clifford-Floquet dynamics, and clarifies the difference between weak and strong thermalization.

Findings

Many states thermalize to infinite temperature

Short-range entangled states approach equilibrium

Distinction between weak and strong thermalization

Abstract

We study the ergodic properties of a unitary Floquet dynamics arising from the repeated application of a translationally-invariant Clifford Quantum Cellular Automata to an infinite system of qubits in d dimensions. One expects that if the QCA does not exhibit any periodicity, a generic initial state of qubits will thermalize, that is, approach the infinite-temperature state. We show that this is true for many classes of states, both pure and mixed. In particular, this is true for all initial states that are short-range entangled and close to the equilibrium state. We also point out a subtle distinction between weak and strong thermalization.