A Decision Procedure for Well-Formed Linear Quantum Cellular Automata

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) in the algebraic model of computation if the input automaton has continuous neighborhood. c © 1997 John Wiley & Sons, Inc.