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.

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

Cited by in corpus (8)

• Entanglement Dynamics in 1D Quantum Cellular Automata
• Quantum phase transition using quantum walks in an optical lattice
• Symmetry-noise interplay in quantum walk on an n-cycle
• Quantum Walks, Weyl equation and the Lorentz group
• When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?
• Generic quantum walk using a coin-embedded shift operator
• Symmetry Protected Topological Phases and Majorana Mode in One-dimensional Quantum Walk with Boundary
• Quantum computing classical physics