A Decision Procedure for Unitary Linear Quantum Cellular Automata

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(n3 ) in the algebraic computational model if the automaton has a continuous neighborhood of size r.

• Type: Journal
• Year: 2002
• Where: SIAMCOMP
• Authors: Christoph Dürr, Miklos Santha
• Keywords: Linear Quantum, Quantum, Quantum Cellular Automata, SIAMCOMP 2002