From gauge transformations to topology computation in quantum lattice gas automata
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.
Keywords
Cite
@article{arxiv.quant-ph/0105087,
title = {From gauge transformations to topology computation in quantum lattice gas automata},
author = {David A. Meyer},
journal= {arXiv preprint arXiv:quant-ph/0105087},
year = {2009}
}
Comments
8 pages, plain TeX, 1 PostScript figure included with epsf.tex (ignore the under/overfull \vbox error messages); for related work see http://math.ucsd.edu/~dmeyer/research.html