Direct Quadratic Minimization Using Magnetic Field-Based Computing

We explore an unconventional front in computing,which we call magnetic field-based computing (MFC), that harnesses the energy minimization aspects of a collection of nanomagnets to solve directly quadratic energy minimization problems, such as those arising in computationaolly intensive computer vision tasks. The Hamiltonian of a collection of bipolar nanomagnets is governed by the pairwise dipolar interactions.The ground state of a nanomagnet collection minimizes this Hamiltonian. We have devised a computational method, based on multi-dimensional scaling, to decide upon the spatial arrangement of nanomagnets that matches a particular quadratic minimization problem. Each variable is represented by a nanomagnet and the distances between them are such that the dipolar interactions match the corresponding pairwise energy term in the original optimization problem. We select the nanomagnets that participate in a specific computation from a field of regularly placed nanomagnets. The nanomagnets that do not participate are deselected using transverse magnetic fields. We demonstrate these ideas by solving Landau-Lifshitz equations as implemented in the NISTpsilas micro-magnetic OOMMF software.