Abstract
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.