One aspect of the present invention includes a Josephson magnetic random access memory (JMRAM) system. The system includes an array of memory cells arranged in rows and columns. Each of the memory cells includes an HMJJD that is configured to store a digital state corresponding to one of a binary logic-1 state and a binary logic-0 state in response to a word-write current that is provided on a word-write line and a bit-write current that is provided on a bit-write line. The HMJJD is also configured to output the respective digital state in response to a word-read current that is provided on a word-read line and a bit-read current that is provided on a bit-read line.