Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 34, Issue 35, Pages 6981-6986Publisher
IOP Publishing Ltd
DOI: 10.1088/0305-4470/34/35/323
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The evolution of a quantum lattice gas automaton (QLGA) for a single charged particle is invariant under multiplication of the wave function by a global phase. Requiring invariance under the corresponding local gauge transformations determines the rule for minimal coupling to an arbitrary external electromagnetic field. We develop the Aharonov-Bohm. effect in the resulting model into a constant time algorithm to distinguish a one-dimensional periodic lattice from one with boundaries; any classical deterministic lattice gas automaton (LGA) algorithm distinguishing these two spatial topologies would have expected running time on the order of the cardinality of the lattice.
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