München 2009 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 1: Quanten- Information, Komplexität
MP 1.3: Vortrag
Montag, 9. März 2009, 17:55–18:15, M010
Invariant states of Clifford Quantum Cellular Automata — •Zoltán Zimborás1, Johannes Gütschow2, Sonja Uphoff2, and Reinhard Werner2 — 1Institut für Theoretische Physik, Universität des Saarlandes, Campus 1, 66041 Saarbrücken, Germany — 2Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstrasse 3, 38106 Braunschweig, Germany
Clifford Quantum Cellular Automata (CQCA) are a special kind of Quantum Cellular Automata for which the so-called Clifford condition ("products of Pauli matrices are mapped to products of Pauli matrices") is satisfied. In this talk we show how one can construct different (product, stabilizer, finitely correlated, quasifree) states that are invariant with respect to a given CQCA action. The possible convergence of non-invariant states to invariant ones under a CQCA action is also discussed. The similarities and differences between CQCA time-evolutions and time-evolutions generated by Hamiltonians (and the differences in the structure of invariant states) are shown by examples. Finally, applications in quantum information theory are outlined.