A building block for hardware belief networks

Belief networks represent a powerful approach to problems involving probabilistic inference, but much of the work in this area is software based utilizing standard deterministic hardware based on the transistor which provides the gain and directionality needed to interconnect billions of them into useful networks. This paper proposes a transistor like device that could provide an analogous building block for probabilistic networks. We present two proof-of-concept examples of belief networks, one reciprocal and one non-reciprocal, implemented using the proposed device which is simulated using experimentally benchmarked models.Comment: Keywords: stochastic, sigmoid, phase transition, spin glass, frustration, reduced frustration, Ising model, Bayesian network, Boltzmann machine. 23 pages, 9 figure

p-Bits for Probabilistic Spin Logic

We introduce the concept of a probabilistic or p-bit, intermediate between the standard bits of digital electronics and the emerging q-bits of quantum computing. We show that low barrier magnets or LBM's provide a natural physical representation for p-bits and can be built either from perpendicular magnets (PMA) designed to be close to the in-plane transition or from circular in-plane magnets (IMA). Magnetic tunnel junctions (MTJ) built using LBM's as free layers can be combined with standard NMOS transistors to provide three-terminal building blocks for large scale probabilistic circuits that can be designed to perform useful functions. Interestingly, this three-terminal unit looks just like the 1T/MTJ device used in embedded MRAM technology, with only one difference: the use of an LBM for the MTJ free layer. We hope that the concept of p-bits and p-circuits will help open up new application spaces for this emerging technology. However, a p-bit need not involve an MTJ, any fluctuating resistor could be combined with a transistor to implement it, while completely digital implementations using conventional CMOS technology are also possible. The p-bit also provides a conceptual bridge between two active but disjoint fields of research, namely stochastic machine learning and quantum computing. First, there are the applications that are based on the similarity of a p-bit to the binary stochastic neuron (BSN), a well-known concept in machine learning. Three-terminal p-bits could provide an efficient hardware accelerator for the BSN. Second, there are the applications that are based on the p-bit being like a poor man's q-bit. Initial demonstrations based on full SPICE simulations show that several optimization problems including quantum annealing are amenable to p-bit implementations which can be scaled up at room temperature using existing technology

Modeling Multi-Magnet Networks Interacting Via Spin Currents

The significant experimental advances of the last few decades in dealing with the interaction of spin currents and nanomagnets, at the device level, has allowed envisioning a broad class of devices that propose to implement information processing using spin currents and nanomagnets. To analyze such spin-magnet logic circuits, in general, we have developed a coupled spin-transport/ magnetization-dynamics simulation framework that could be broadly applicable to various classes of spin-valve/ spin-torque devices. Indeed, the primary purpose of this chapter is to describe in detail, the overall approach we have developed to include a description of spin transport coupled with magnetization dynamics and to show how it was benchmarked against available data on experiments. We address non-collinear spin-transport in Section-2 using a lumped "4-component spin-circuit formalism" that describes the interaction of non-collinear magnets (required for modeling spin torque), by computing 4-component currents and voltages at every node of a "circuit". For modeling the magnetization dynamics, we use the standard Landau-Lifshitz-Gilbert (LLG) equation with the Slonczewski and the field-like terms included for spin torque. Section-3 describes how this LLG model is coupled with the spin transport model to analyze spin-torque experiments and spin-magnet circuits in general. We include MATLAB codes in the Appendix to facilitate a "hands-on" understanding of our model and hope it will enable interested readers to conveniently analyze their own experiments, develop a deeper insight into spin-magnet circuits or come up with their own creative designs.Comment: To appear in Handbook of Spintronics, eds. D Awschalom, J Nitta & Y Xu, Springer (2013). 52 pages and 20 figures. Comments and suggestions are welcome. Code typos corrected in (v3