Hannover 2010 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 40: Quantum Information: Quantum Computing

Q 40.6: Talk

Wednesday, March 10, 2010, 17:45–18:00, F 128

The fractal structure of Clifford cellular automata — •Vincent Nesme, Johannes Gütschow, and Reinhard Werner — Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover

It is a well-known fact that the spacetime diagrams of some cellular automata have a fractal struc- ture: for instance Pascal*s triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular automata is a much explored topic, but virtually all of the results revolve around a special class of automata, whose main features include being irreversible, being defined on an alphabet having a ring structure and respecting this structure, and fulfilling a property known as being (weakly) p-Fermat. The class of automata that we study in this article fulfills none of these properties. The cell structure is weaker, as it does not come with a multiplication, may very well be reversible *and* interesting, and they are typically far from being p-Fermat, even weakly. However, they do produce fractal spacetime diagrams, and we will explain why and how. These automata emerge naturally from the field of quantum cellular automata, as they include the classical equivalent of the Clifford quantum cellular automata, which have been studied by the quan- tum community for several reasons. They provide a universal model of quantum computation, and they can be used to generate highly entangled states, to use as a primary resourse for measurement- bases models of quatum computing.