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The evolution of a quantum lattice gas automaton (LGA) for a single chargedparticle is invariant under multiplication of the wave function by a globalphase. Requiring invariance under the corresponding local gauge transformationsdetermines the rule for minimal coupling to an arbitrary externalelectromagnetic field. We develop the Aharonov-Bohm effect in the resultingmodel into a constant time algorithm to distinguish a one dimensional periodiclattice from one with boundaries; any classical deterministic LGA algorithmdistinguishing these two spatial topologies would have expected running time onthe order of the cardinality of the lattice.

From gauge transformations to topology computation in quantum lattice gas automata