D. Meyer. From quantum cellulax automata to quantum lattice gases. Journal of Statistical Physics, 85:551-574, 1996. Also available from the Los Alamos Preprint Archive, quant-ph/9604003.  Home/Search   Document Not in Database   Summary   Related Articles

....impossible, since the global process is necessarily non unitary. It is also easy to verify that the only possible translationally invariant unitary processes on the line allowing only transitions between adjacent lattice sites are the left and right shift operators, up to an overall phase [24]. These processes simply correspond to motion in a single direction. If the particle has an extra degree of freedom that assists in its motion, however, then it is possible to construct more interesting translation invariant local unitary processes. Consider a quantum particle that moves freely ....

....[4, 5] This gives another asymptotic form for the probability distribution. The SchrSdinger approach is also quite general and could be potentially applied to quantum walks on any Cayley graph. Related work Various quantum variants of random walks have previously been studied by a few authors [6, 12, 24, 32], but their results are, for the most part, unrelated to ours. The first study of quantum walks is apparently due to Meyer [24] Meyer s model (quantum lattice gas automata or QLGA) is equivalent to our two way infinite Hadamard walk, but he addresses different questions than the ones we ....

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D. Meyer. From quantum cellulax automata to quantum lattice gases. Journal of Statistical Physics, 85:551-574, 1996. Also available from the Los Alamos Preprint Archive, quant-ph/9604003.

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