Algebraic and Boolean Methods for SFQ Superconducting Circuits

Rapid single-flux quantum (RSFQ) is one of the most advanced and promising superconducting logic families, offering exceptional energy efficiency and speed. RSFQ technology requires delay registers (DFFs) and splitter cells to satisfy the path-balancing and driving-capacity constraints. In this paper, we present a comprehensive exploration of methods for synthesizing and optimizing SFQ circuits. Our approach includes algebraic and Boolean optimization techniques that work on the xor-and graph (XAG) representation of combinational logic. Additionally, we introduce a technology mapping method to satisfy the path-balancing and fanout constraints while minimizing the area. Finally, we propose a synthesis flow for SFQ circuits. In the experimental results, we show an average reduction in the area and delay of 43% and 34%, respectively, compared to the state-of-the-art.