Direct Quadratic Minimization Using Magnetic Field-Based Computing

Direct Quadratic Minimization Using Magnetic Field-Based Computing Sarkar, S. Bhanja, S. Dept. of Comput. Sci. & Eng., South Univ., Tampa, FL This paper appears in: Design and Test of Nano Devices, Circuits and Systems, 2008 IEEE International Workshop on Publication Date: 29-30 Sept. 2008 On page(s): 31 - 34 Location: Cambridge, MA ISBN: 978-0-7695-3379-7 Digital Object Identifier: 10.1109/NDCS.2008.13 Current Version Published: 2008-10-03

Abstract 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.

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