From quantum cellular automata to quantum lattice gases View Full Text


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Article Info

DATE

1996-12

AUTHORS

David A. Meyer

ABSTRACT

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, 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. More... »

PAGES

551-574

References to SciGraph publications

  • 1984-03. Computation theory of cellular automata in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1982-04. New computer architectures and their relationship to physics or why computer science is no good in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1982-06. Simulating physics with computers in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1992-08. Lattice gases and exactly solvable models in JOURNAL OF STATISTICAL PHYSICS
  • 1994-04. Quantum mechanics on a space-time lattice using path integrals in a minkowski metric in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1987-10. Cellular automata and statistical mechanical models in JOURNAL OF STATISTICAL PHYSICS
  • 1980-05. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines in JOURNAL OF STATISTICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02199356

    DOI

    http://dx.doi.org/10.1007/bf02199356

    DIMENSIONS

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