Improving Synthesis of Reversible Circuits: Exploiting Redundancies in Paths and Nodes of QMDDs

In recent years, reversible circuits have become an established emerging technology through their variety of applications. Since these circuits employ a completely different structure from conventional circuitry, dedicated functional synthesis algorithms have been proposed. Although scalability has been achieved by using approaches based on decision diagrams, the resulting circuits employ a significant complexity measured in terms of quantum cost. In this paper, we aim for a reduction of this complexity. To this end, we review QMDD-based synthesis. Based on that, we propose optimizations that allow for a substantial reduction of the quantum costs by jointly considering paths and nodes in the decision diagram that employ a certain redundancy. In fact, in our experimental evaluation, we observe substantial improvements of up to three orders of magnitudes in terms of runtime and up to six orders of magnitudes (a factor of one million) in terms of quantum cost.