On Quantum Cellular Automata
Abstract
Description
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.
LaTeX (amsmath, amssymb, graphicx packages) 17 pages, 22 eps figures; v2: misspelling corrected, +2 figures
LaTeX (amsmath, amssymb, graphicx packages) 17 pages, 22 eps figures; v2: misspelling corrected, +2 figures