High-Density Superconductive Logic Circuits Utilizing 0 and $\pi$ Josephson Junctions

Superconductor Electronics (SCE) is a fast and power-efficient technology with great potential for overcoming conventional CMOS electronics' scaling limits. Nevertheless, the primary challenge confronting SCE today pertains to its integration level, which lags several orders of magnitude behind CMOS circuits. In this study, we have innovated and simulated a novel logic family grounded in the principles of phase shifts occurring in 0 and $\pi$ Josephson junctions. The fast phase logic (FPL) eliminates the need for large inductor loops and shunt resistances by combining the half-flux and phase logic. Therefore, the Josephson junction (JJ) area only limits the integration density. The cells designed with this paradigm are fast, and the clock-to-Q delay is about 4ps while maintaining over 50% parameter margins. This logic is power efficient and can increase the integration by at least 100$\times$ in the SCE chips.