Hierarchical synthesis of reversible circuits using positive and negative Davio decomposition

Synthesis of reversible circuits is an important research area providing the basis for a design flow of this emerging technology. Recently, in the development of scalable synthesis approaches a significant step forward has been made by a hierarchical method in combination with Shannon decomposition. However, this approach leads to circuits with high costs. In this paper, we propose an alternative that additionally makes use of positive Davio and negative Davio decomposition. We show that the usage of these decomposition types offers several advantages for the synthesis of reversible circuits. Using the proposed approach, on average the number of lines can be reduced by 22%, the number of gates by 22%, and the quantum cost by 32%. In the best case, even reductions of more than 60% are possible.