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From gauge transformations to topology computation in quantum lattice gas automata

David A. Meyer
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Abstract

The evolution of a quantum lattice gas automaton (LGA) 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 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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David A. Meyer. 2001-05-17. From gauge transformations to topology computation in quantum lattice gas automata. https://doi.org/10.1088/0305-4470%2F34%2F35%2F323

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