dorsal/arxiv
View SchemaFrom quantum cellular automata to quantum lattice gases
| Authors | David A. Meyer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9604003 |
| URL | https://arxiv.org/abs/quant-ph/9604003 |
| DOI | 10.1007/BF02199356 |
| Journal | J. Stat. Phys. 85 (1996) 551-574 |
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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"abstract": "A natural architecture for nanoscale quantum computation is that of a quantum\ncellular automaton. Motivated by this observation, in this paper we begin an\ninvestigation of exactly unitary cellular automata. After proving that there\ncan be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in\none dimension, we weaken the homogeneity condition and show that there are\nnontrivial, exactly unitary, partitioning cellular automata. We find a one\nparameter family of evolution rules which are best interpreted as those for a\none particle quantum automaton. This model is naturally reformulated as a two\ncomponent cellular automaton which we demonstrate to limit to the Dirac\nequation. We describe two generalizations of this automaton, the second of\nwhich, to multiple interacting particles, is the correct definition of a\nquantum lattice gas.",
"arxiv_id": "quant-ph/9604003",
"authors": [
"David A. Meyer"
],
"categories": [
"quant-ph",
"comp-gas",
"hep-th",
"nlin.CG"
],
"doi": "10.1007/BF02199356",
"journal_ref": "J. Stat. Phys. 85 (1996) 551-574",
"title": "From quantum cellular automata to quantum lattice gases",
"url": "https://arxiv.org/abs/quant-ph/9604003"
},
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