2009/06/30 by Johannes Gütschow, Sonja Uphoff, Reinhard F. Werner +1
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Cellular Automata and Applications #Cellular automaton #Fractal #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum cellular automaton #Quantum chaos and dynamical systems #Quantum computer #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Time evolution #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.3278513
published as J. Math. Phys. 51, 015203 (2010) · published version; edited some proofs (esp. for Lemma 4.9) and corrected typos
openalex publication_date 2010/01/01 · arxiv created 2010/02/01 · arxiv updated 2010/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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, such as quasifree and stabilizer states. Finally, we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.