Journal of Statistical Physics

, Volume 85, Issue 5, pp 551-574

First online:

From quantum cellular automata to quantum lattice gases

  • David A. MeyerAffiliated withProject in Geometry and Physics, Department of Mathematics, University of California-San Diego

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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.

Key Words

Quantum cellular automaton quantum lattice gas quantum computation