Comparison of the Cost Metrics through Investigation of the Relation between Optimal NCV an.pdfVIP

Comparison of the Cost Metrics through Investigation of the Relation between Optimal NCV and Optimal NCT 3-qubit Reversible Circuits Dmitri Maslov 1 and D. Michael Miller 2 dmitri.maslov@, mmiller@cs.uvic.ca 1 Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada 2 Department of Computer Science, University of Victoria, Victoria, BC, V8W 3P6, Canada December 4, 2006 Abstract A breadth-first search method for determining optimal 3-qubit circuits composed of quantum NOT, CNOT, controlled-V and controlled-V + (NCV) gates is introduced. Results are presented for simple gate count and for technology motivated cost metrics. The optimal NCV circuits are also compared to NCV circuits derived from optimal NOT, CNOT and Toffoli (NCT) gate circuits. The work presented here provides basic results and motivation for continued study of the direct synthesis of NCV circuits, and establishes relations between function realizations in different circuit cost metrics. 1 Introduction Reversible and quantum logic synthesis have attracted recent attention as a result of advances in quantum and nano technologies. Many of the proposed synthesis methods, especially in the area of reversible logic synthesis, assume large gate libraries where implementation costs of the gates may vary significantly. However, these methods most often target minimization of the gate count. Use of such a circuit cost metric is likely to result in seemingly small circuits, which are in fact expensive to construct. The synthesis of circuits composed of NOT, CNOT and Toffoli (NCT) gates [18] and multiple control Toffoli gates [1, 5, 10, 11, 20] has recently been extensively studied. Converting an NCT or a multiple control Toffoli gate circuit into one composed of NOT, CNOT, controlled-V and controlled-V + (NCV) gates has also been considered 1 [2, 9]. Further simplification of NCV circuits has also been well studied [9]. It is an important question how close the circuits found by the