A decision procedure for unitary linear quantum cellular automata

Authors:
C. Durr
Affiliations:
-
Venue:
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Year:
1996

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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(4r-3)/(r+1))=O(n/sup 4/) if the automaton has a continuous neighborhood of size r.