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      From quantum cellular automata to quantum lattice gases

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          Abstract

          A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.

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          Confinement of quarks

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            Space-time as a causal set

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              Lattice fermions

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                Author and article information

                Journal
                04 April 1996
                1996-11-13
                Article
                10.1007/BF02199356
                quant-ph/9604003
                1c969edb-1bf1-47a7-a919-a67151f046cb
                History
                Custom metadata
                J. Stat. Phys. 85 (1996) 551-574
                22 pages, plain TeX, 9 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); minor typographical corrections and journal reference added
                quant-ph comp-gas hep-th nlin.CG

                Quantum physics & Field theory,High energy & Particle physics,Nonlinear & Complex systems

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