A pre-optimization technique to generate initial reversible circuits with low quantum cost

In order to generate an initial reversible/quantum circuit to realize a given Boolean function, one of the major approaches is to find a small Exclusive-or Sum-Of-Products (ESOP) expression for the function; each product term in the ESOP expression naturally corresponds to a single Mixed Polarity Multiple-Control Toffoli (MPMCT) gate. In this paper, we propose a technique to perform pre-optimization before generating an ESOP expression. Our approach is unique in a sense that instead of finding a small ESOP expression for a given function, we try to change it by adding MPMCT gates so that the modified function has a smaller ESOP expression. We expect that our approach can generate a better initial circuit compared to using ESOP minimization techniques only. Indeed our preliminary experiments for small functions confirm this expectation. Thus, we expect that our approach would be a good pre-optimization technique that can be used with most existing reversible circuit synthesis techniques.