Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata
Quantum Physics
2010-02-01 v2 Statistical Mechanics
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0906.3195,
title = {Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata},
author = {Johannes Gütschow and Sonja Uphoff and Reinhard F. Werner and Zoltán Zimborás},
journal= {arXiv preprint arXiv:0906.3195},
year = {2010}
}
Comments
published version; edited some proofs (esp. for Lemma 4.9) and corrected typos