Phase logic based on $\pi$ Josephson junctions

The transition to Josephson digital circuits with the representation of information in the form of phase jumps of the superconducting order parameter on heterostructures promises a radical increase in the degree of integration while maintaining high speed and energy efficiency. However, it is not yet possible to manufacture reproducible bistable Josephson junctions, which are necessary for the functioning of the previously proposed basic units of the phase logic. To solve this problem, the concept of phase logic based on $\pi$ junctions is proposed and analyzed within the resistive model of Josephson heterostructures. The potential energy of such junctions has a single minimum, with a difference in the order parameters of the electrodes equal to $\pi$. It is demonstrated that the use of $\pi$ junctions allows one to implement the entire set of logic devices necessary for the operation of digital computing devices based on phase logic.