Optimizing the Mapping of Reversible Circuits to Four-Valued Quantum Gate Circuits

This paper considers the optimization of reversible circuits composed of multiple-control Toffoli gates to quantum circuits using the well-known NCV-1 (NCV) library and the recently introduced NCV-v1 library which both use a four-valued model for the quantum gates. The techniques introduced handle positive and negative controls which are central to many reversible circuit synthesis procedures. Experimental results confirm the methods are applicable to circuits obtained by diverse synthesis methods. The results also show the significant advantage of the NCV-v1 library.