München 2009 – scientific programme

Parts | Days | Selection | Search | Downloads | Help

MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Quanten- Information, Komplexität

MP 1.3: Talk

Monday, March 9, 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.