A decision procedure for unitary linear quantum cellular automata

Details A decision procedure for unitary linear quantum cellular automata A decision procedure for unitary linear quantum cellular automata

1996-04-09

arxiv.org/abs/quant-ph/9604007v5

Proceeding of the 37th IEEE Symposium on Foundations of Computer Science, 38--45, 1996

Physics

Quantum Physics

Updated for submission to SIAM Journal on Computing. Improved slightly the algorithm

Scientific paper

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(n^3) 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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