Synthesis of Reversible Circuits Based on Products of Exclusive OR Sums

This paper introduces a new synthesis approach called Products of EXOR-sums (POE) and demonstrates its utility when employed in an Exclusive-Or-Sum-of-Products (ESOP) based algorithm for reversible and permutative quantum circuits restricted to single output functions. Unlike previous ESOP approaches such as EXORCISM-4 which realize functions as an EXOR-ed sum of product literals, this new algorithm realizes functions as an EXOR-ed sum of POEs (EPOE). A comparison of EXORCISM-4 and EPOE circuits shows that the latter approach often produces circuits with significantly lower quantum costs.