Evaluating ESOP optimization methods in quantum compilation flows

Abstract

Exclusive-or sum-of-products (ESOP) expressions are used as intermediate representations in quantum circuit synthesis flows, and their complexity impacts the number of gates of the resulting circuits. Many state-of-the-art techniques focus on minimizing the number of product terms in a ESOP expression, either exactly or in a heuristic fashion. In this paper, we investigate into ESOP optimization considering two recent quantum compilation flows with opposite requirements. The first flow generates Boolean functions with a small number of Boolean variables, which enables the usage of methods from exact synthesis; the second flow generates Boolean functions with many Boolean variables, such that heuristics are more effective. We focus on the reduction of the number of T gates, which are expensive in fault-tolerant quantum computing and integrate ESOP optimization methods into both flows. We show an average reductions of 36.32% in T-count for the first flow, while in the second flow an average reduction of 28.23% is achieved.