A complete set of transformation rules for quantum Boolean circuits with CNOT gates

This paper gives a simple but nontrivial set of local transformation rules for CNOT-based quantum circuits. It is shown that this rule set is complete, namely for any two equivalent circuits, S-1 and S-2, there is a sequence of transformations, each of them in the rule set, which changes S-1 to S-2. This rule set can be used for incremental circuit optimization methods like the classical circuit design methodology. (C) 2002 Elsevier Science Ltd. All rights reserved.