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A decision procedure for unitary linear quantum cellular automata

Christoph Durr, Miklos Santha

quant-pharXiv:quant-ph/9604007

Abstract

Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution operator has to be a unitary transformation. In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary. The complexity of the algorithm is O(n((3r-1)/(r+1))) = O(n3) in the algebraic computational model if the automaton has a continuous neighborhood of size r, where n is the size of the input.

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