A memory system comprising: an array of memory cells (522, 524, 526, 538) 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 (522, 528, 534) in at least one row of the array of memory cells (522, 524, 526, 538); a set of return word-lines, wherein each of the set of return word-lines is coupled to the first plurality of memory cells (522, 528, 534) in the at least one row of the array of memory cells (522, 524, 526, 538); and a set of bit-lines, wherein each of the set of the bit-lines is coupled to a second plurality of memory cells (522, 524, 526) in at least one column of the array of memory cells (522, 524, 526, 538), wherein each of the first plurality of the memory cells (522, 528, 534) and each of the second plurality of the memory cells (522, 524, 526) 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 (522, 524, 526, 538) 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 (522, 528, 534) in at least one row of the array of memory cells (522, 524, 526, 538); a set of return word-lines, wherein each of the set of return word-lines is coupled to the first plurality of memory cells (522, 528, 534) in the at least one row of the array of memory cells (522, 524, 526, 538); and a set of bit-lines, wherein each of the set of the bit-lines is coupled to a second plurality of memory cells (522, 524, 526) in at least one column of the array of memory cells (522, 524, 526, 538), wherein each of the first plurality of the memory cells (522, 528, 534) and each of the second plurality of the memory cells (522, 524, 526) 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.