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arXiv quant-ph/04061192004-06-24quant-phcs.OHnlin.CG

On Quantum Cellular Automata

Alexander Yu. Vlasov

备注：: LaTeX (amsmath, amssymb, graphicx packages) 17 pages, 22 eps figures; v2: misspelling corrected, +2 figures

英文摘要：

In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and so there is a question about quantum CA derived from more general, standard model of classical CA. In present work is considered an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules. It is used language of vectors in Hilbert spaces instead of C*-algebras, but results may be compared in some cases. Finally, the quantum lattice gases, quantum walk and "bots" are also discussed briefly.

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