A hierarchical distributed linear evolutionary system for the synthesis of 4-bit reversible circuits

Abstract

Even limited to 4-bits reversible functions, the synthesis of optimal reversible circuits becomes an arduous task owing to the extremely large problem space. The current paper tries to answer the following question: is it possible to implement optimal 4-bit reversible circuits without relying on existing partial solutions libraries? A distributed linear genetic programming based-approach (DRIMEP2) is presented. It consists of a hierarchical topology with a new communication policy to allow the evolutionary algorithm to explore and exploit the search space in an efficient way. To test the effectivity and the efficiency of the proposed system, the design of 69 benchmarks (4-bits reversible functions) was performed. With respect to good results available in the literature, a gate count reduction up to 60% was achieved with an average of 16.82% (for the two first benchmark groups where the gate count of the circuit was considered by the reference authors) and a quantum cost reduction up to 62.71% was reached with an average of 10.79% (for the two remaining benchmark groups where the quantum cost of the circuit was considered by the reference authors).