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An algebraic study of unitary one dimensional quantum cellular automata

Pablo Arrighi
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Abstract

We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata's computational power. The configurations we consider have finite but unbounded size.

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Pablo Arrighi. 2005-12-05. An algebraic study of unitary one dimensional quantum cellular automata. https://arxiv.org/abs/quant-ph/0512040

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