On the structure of Clifford quantum cellular automata Export

@article{citeulike:2734399, abstract = {We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli 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 every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single Clifford cellular automaton timestep, thereby characterizing these class of stabilizer states, and we show that all 1D Clifford quantum cellular automata are generated by a few elementary operations. We also show that the correspondence between translationally invariant stabilizer states and translationally invariant Clifford operations holds for periodic boundary conditions.}, archivePrefix = {arXiv}, author = {Dirk-M and Vogts, Holger and Werner, Reinhard F.}, citeulike-article-id = {2734399}, citeulike-linkout-0 = {http://arxiv.org/abs/0804.4447}, citeulike-linkout-1 = {http://arxiv.org/pdf/0804.4447}, day = {28}, eprint = {0804.4447}, keywords = {automata, cellular}, month = {Apr}, posted-at = {2009-10-26 16:04:32}, priority = {3}, title = {On the structure of Clifford quantum cellular automata}, url = {http://arxiv.org/abs/0804.4447}, year = {2008} }

TY - JOUR ID - citeulike:2734399 L3 - citeulike-article-id:2734399 N2 - We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli 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 every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single Clifford cellular automaton timestep, thereby characterizing these class of stabilizer states, and we show that all 1D Clifford quantum cellular automata are generated by a few elementary operations. We also show that the correspondence between translationally invariant stabilizer states and translationally invariant Clifford operations holds for periodic boundary conditions. TI - On the structure of Clifford quantum cellular automata KW - automata KW - cellular AU - Dirk-M AU - Vogts, Holger AU - Werner, Reinhard PY - 2008/Apr/28/ UR - http://arxiv.org/abs/0804.4447 ER -