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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 e#ect in the resulting model into a constant time algorithm to distinguish a one dimensional periodic lattice from one with boundaries; any classical ... (Update)
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BibTeX entry: (Update)
D. A. Meyer, "From gauge transformations to topology computation in quantum lattice gas automata", J. Phys. A: Math. Gen. 34 (2001) 6981--6986. http://citeseer.ist.psu.edu/meyer00from.html More
@misc{ meyer01from,
author = "D. Meyer",
title = "From gauge transformations to topology computation in quantum lattice gas
automata",
text = "D. A. Meyer, From gauge transformations to topology computation in quantum
lattice gas automata, J. Phys. A: Math. Gen. 34 (2001) 6981--6986.",
year = "2001",
url = "citeseer.ist.psu.edu/meyer00from.html" }
Citations (may not include all citations):210 A fast quantum mechanical algorithm for database search - Grover - 1996
168 Algorithms for quantum computation: discrete logarithms and .. - Shor - 1994
22 From quantum cellular automata to quantum lattice gases - Meyer - 1996
13 Quantum mechanics of lattice gas automata: One-particle plan.. - Meyer - 1997
12 Simulating quantum mechanics on a quantum computer - Boghosian, Taylor - 1998
12 A quantum lattice-gas model for the manyparticle Schrodinger.. (context) - Boghosian, Taylor - 1997
8 The quantum theory of the electron (context) - Dirac - 1928
7 Spectral asymmetry and Riemannian geometry. III (context) - Atiyah, Patodi et al. - 1976
6 Significance of electromagnetic potentials in the quantum th.. (context) - Aharonov, Bohm - 1959
6 Discrete fluids (context) - Hasslacher - 1988
6 Quantum lattice gases and their invariants - Meyer - 1997
3 Quantum mechanics of lattice gas automata: Boundary conditio.. (context) - Meyer - 1998
3 Poly-locality in quantum computing (context) - Freedman
2 Topological Algorithms for Digital Image Processing (context) - Kong, Rosenfeld - 1996
1 Does Rydberg state manipulation equal quantum computation (context) - Meyer, Kwiat et al. - 2000
1 E#cient networks for quantum factoring (context) - See, Beckman et al. - 1996
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