Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
C. Durr , Lab. de Recherche en Inf., Univ. de Paris-Sud, Orsay, France
M. Santha , Lab. de Recherche en Inf., Univ. de Paris-Sud, Orsay, France
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.
cellular automata; cellular automata; linear quantum; unitary; quantum computing; complexity; decision procedure
C. Durr and M. Santha, "A decision procedure for unitary linear quantum cellular automata," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 38.