Transformation rules for designing CNOT-based quantum circuits

This paper gives a simple but nontrivial set of local transformation rules for Control-NOT(CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S1 and S2, there is a sequence of transformations, each of them in the rule set, which changes S1 to S2. Our motivation is to use this rule set for developing a design theory for quantum circuits whose Boolean logic parts should be implemented by CNOT-based circuits. As a preliminary example, we give a design procedure based on our transformation rules which reduces the cost of CNOTbased circuits. Categories and Subject Descriptors B.6.m [LOGIC DESIGN]: Miscellaneous General Terms Design, Theory Keywords Quantum Circuit, CNOT Gate, Local Transformation Rules

• Type: Conference
• Year: 2002
• Where: DAC
• Authors: Kazuo Iwama, Yahiko Kambayashi, Shigeru Yamashita
• Keywords: Control-NOT(CNOT)-based Combinatorial Circuits, DAC 2002, Design Automation, Local Transformation Rules, Rule Set