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Remarks on the Structure of Clifford Quantum Cellular Automata

Dirk-Michael Schlingemann

ISI Foundation, Viale S. Severo 65, 10133 Torino, Italy

https://doi.org/10.1142/S1230161209000207Cited by:0 (Source: Crossref)

Abstract

We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite abelian symplectic group) are mapped to multiples of tensor products of Weyl operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection-invariant with respect to the origin. In the one-dimensional case we also find that all 1D Clifford quantum cellular automata are generated by a few elementary operations.

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Vol. 16, No. 02n03

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Received 1 December 2008

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Remarks on the Structure of Clifford Quantum Cellular Automata

Abstract

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