David A Meyer 2001 J. Phys. A: Math. Gen. 34 6981 doi:10.1088/0305-4470/34/35/323
From gauge transformations to topology computation in quantum lattice gas automata
David A Meyer1,2
Show affiliationsThe 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.
- PACS
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03.67.Lx Quantum computation architectures and implementations
41.20.-q Applied classical electromagnetism
02.40.-k Geometry, differential geometry, and topology
- MSC
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81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
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Accelerators, beams and electromagnetism
- Dates
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Issue 35 (7 September 2001)
Received 21 November 2000
Published 24 August 2001
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From gauge transformations to topology computation in quantum lattice gas automata
David A Meyer 2001 J. Phys. A: Math. Gen. 34 6981
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