A magnetic system for solving a quadratic optimization problem by associating each of a plurality of variables of a quadratic optimization problem with a nanomagnet of a nanomagnet array, driving the nanomagnets of the nanomagnet array to an excited state, allowing the nanomagnets of the nanomagnet array to enter a relaxed state after being driven to an excited state, wherein the nanomagnets magnetically couple with one another in the relaxed state to minimize the total magnetic coupling energy of the nanomagnet array, and sensing a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem.