A memory system comprising: an array of memory cells arranged in rows and columns; a set of word-lines, wherein each of the set of the word-lines is coupled to a first plurality of memory cells in at least one row of the array of memory cells ; a set of return word-lines, wherein each of the set of return word-lines is coupled to the first plurality of memory cells in the at least one row of the array of memory cells ; and a set of bit-lines, wherein each of the set of the bit-lines is coupled to a second plurality of memory cells in at least one column of the array of memory cells , wherein each of the first plurality of the memory cells and each of the second plurality of the memory cells comprises: at least one memory storage element comprising at least one readout superconducting quantum interference device, SQUID, and a magnetic Josephson Junction, MJJ, , and wherein the at least one memory storage element further comprises a differential transformer coupled in series with the MJJ such that in response to a bit-line current applied to at least one of the set of the bit-lines and a word-line current applied to at least one of the set of word-lines coupled to at least one of the set of return word lines, the differential transformer is configured to induce a flux in the at least one readout SQUID, wherein the at least one readout SQUID comprises a first Josephson junction, JJ, and a second Josephson junction, JJ, , and wherein the differential transformer comprises a first primary coupling coupled to the at least one of the set of word lines and a second primary coupling coupled to the at least one of the set of the return word-lines. an array of memory cells arranged in rows and columns; a set of word-lines, wherein each of the set of the word-lines is coupled to a first plurality of memory cells in at least one row of the array of memory cells ; a set of return word-lines, wherein each of the set of return word-lines is coupled to the first plurality of memory cells in the at least one row of the array of memory cells ; and a set of bit-lines, wherein each of the set of the bit-lines is coupled to a second plurality of memory cells in at least one column of the array of memory cells , wherein each of the first plurality of the memory cells and each of the second plurality of the memory cells comprises: at least one memory storage element comprising at least one readout superconducting quantum interference device, SQUID, and a magnetic Josephson Junction, MJJ, , and wherein the at least one memory storage element further comprises a differential transformer coupled in series with the MJJ such that in response to a bit-line current applied to at least one of the set of the bit-lines and a word-line current applied to at least one of the set of word-lines coupled to at least one of the set of return word lines, the differential transformer is configured to induce a flux in the at least one readout SQUID, wherein the at least one readout SQUID comprises a first Josephson junction, JJ, and a second Josephson junction, JJ, , and wherein the differential transformer comprises a first primary coupling coupled to the at least one of the set of word lines and a second primary coupling coupled to the at least one of the set of the return word-lines. <EOS>