  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.
