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A decision procedure for well-formed linear quantum cellular automata

Christoph Durr·Huong LeThanh·Miklos Santha
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Abstract

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is $O(n^2)$ in the algebraic model of computation if the input automaton has continuous neighborhood.

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Christoph Durr, Huong LeThanh, Miklos Santha. 2000-10-27. A decision procedure for well-formed linear quantum cellular automata. https://arxiv.org/abs/cs/9906024

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