Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata

TL;DR

This paper analyzes the complex asymptotic behavior and entanglement generation of Clifford Quantum Cellular Automata, highlighting their potential for universal quantum computation and classifying their dynamic properties.

Contribution

It provides a detailed classification of CQCAs, studies invariant states and convergence, and analytically and numerically examines entanglement generation in stabilizer and quasifree states.

Findings

Identification of invariant states for different CQCAs

Analysis of convergence properties of state classes

Quantitative results on entanglement growth in stabilizer and quasifree states

Abstract

We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, like quasifree and stabilizer states. Finally we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.