Improved NCV Gate Realization of Arbitrary Size Toffoli Gates

Abstract

The problem of synthesis and optimization of reversible and quantum circuits have drawn the attention of researchers in recent years. The typical design flow for such circuits first carries out the step of synthesis in terms of reversible gates, and then maps (decomposes) each reversible gate into equivalent set of quantum gates (e.g. from the NCV library). Since its initial proposal in realizing a Toffoli gate using quantum gates, several structural modifications have been proposed in the literature in order to reduce the cost of the generated netlist. The most recently introduced approach produces improved NCV cascade successively by partitioning the control lines of the given Toffoli gate in all possible ways, and replacing intermediate Toffoli gates with optimized equivalent NCV cascades form a catalog. In this approach the complexity of decomposing large Toffoli gates is high. In the present paper an efficient heuristic for partitioning the control lines of a given Toffoli gate is proposed. This heuristic is used for decomposition of the Toffoli gate without using any NCV catalog, after applying a template based optimization step. The cost of resultant circuit is similar to or sometimes better than the one reported by previous approaches.