Physics – Quantum Physics
Scientific paper
1996-04-04
J. Stat. Phys. 85 (1996) 551-574
Physics
Quantum Physics
22 pages, plain TeX, 9 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); minor typog
Scientific paper
10.1007/BF02199356
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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