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Quantization of cellular automata

Abstract : Take a cellular automaton, consider that each configuration is a basis vector in some vector space, and linearize the global evolution function. If lucky, the result could actually make sense physically, as a valid quantum evolution; but does it make sense as a quantum cellular automaton? That is the main question we address in this paper. In every model with discrete time and space, two things are required in order to qualify as a cellular automaton: invariance by translation and locality. We prove that this locality condition is so restrictive in the quantum case that every quantum cellular automaton constructed in this way - i.e., by linearization of a classical one - must be reversible. We also discuss some subtleties about the extent of nonlocality that can be encountered in the one-dimensional case; we show that, even when the quantized version is non local, still, under some conditions, we may be unable to use this nonlocality to transmit information nonlocally.
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Submitted on : Thursday, April 17, 2008 - 12:30:21 AM
Last modification on : Friday, July 17, 2020 - 11:10:21 AM
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  • HAL Id : hal-00274002, version 1



Pablo Arrighi, Vincent Nesme. Quantization of cellular automata. JAC 2008, Apr 2008, Uzès, France. pp.204-215. ⟨hal-00274002⟩



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