Scaling-up ESOP Synthesis for Quantum Compilation

Abstract

Today's rapid advances in quantum computing hardware call for scalable synthesis methods to map combinational logic represented as multi-level Boolean networks (e.g., an and-inverter graph, AIG) to quantum circuits. Such synthesis process must yield reversible logic function since quantum circuits are reversible. Thus, logic representations using exclusive sum-of-products (ESOP) are advantageous because of their natural relation to Toffoli gates, one of the primitives in reversible logic. This motivates developing effective methods to collapse AIG logic networks into ESOPs. In this work, we present two state-of-the-art methods to collapse an AIG into an ESOP expression, describe their shortcomings and introduce a new approach based on the divide-and-conquer paradigm. We demonstrate the effectiveness of our method in collapsing IEEE-compliant half precision floating point networks. Results show that our method can collapse designs-which were previously not solvable within a week-in less than 5 minutes. We also describe a technique capable of taking advantage of this new method to generate quantum circuits with up to 50% fewer $T$ gates compared to state-of-the-art methods.