Improving the quantum cost of reversible Boolean functions using reorder algorithm

This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed–Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decrease the quantum cost of the reversible circuit. The paper achieves a decrease in the quantum cost and/or the circuit length, on average, when compared with relevant work in the literature.