Josephson junction based memory devices and methods for their use are described herein. An example Josephson junction based memory device includes a plurality of superconducting loops. Each superconducting loop includes at least one Josephson junction. The plurality of superconducting loops are electrically coupled. The plurality of superconducting loops include a plurality of input loops, a plurality of readout loops, and at least one shared loop. The plurality of superconducting loops are configured to store or annihilate magnetic flux quanta in one or more of the superconducting loops in response to a combination of control signals and single flux quantum (SFQ) pulses.