A reversible superconducting circuit includes two Josephson transmission lines. Inductors connect Josephson Junctions in the array. Each transmission line passes a fluxon along the Junctions. The circuit includes an interface with first and second shunt capacitors coupled to the first and second transmission lines, and a third shunt capacitor, forming a connecting circuit with the first and second shunt capacitors. The shunt capacitors include Josephson junctions in parallel. The connecting circuit receives an input fluxon and transmits an output fluxon. The circuit also includes a Josephson Junction and inductor in parallel with the third shunt capacitor, forming a storage circuit. The storage circuit stores a SFQ. The output fluxon has polarity based on the SFQ stored when the first fluxon is received. The input fluxon causes the polarity of the stored SFQ to be the same as the polarity of the input fluxon, immediately after the input fluxon is received.