Beyond Ising: Mixed Continuous Optimization with Gaussian Probabilistic Bits Using Stochastic MTJs

Dedicated Ising Machines tailored to solve hard computational problems have generated significant attention. Despite their promise, virtually all existing Ising Machines use binary variables (0 or 1), severely limiting their applicability in practical problems that often require continuous (or multi-state) variables. Here, we experimentally demonstrate contin-uous probabilistic bits in a network-of-networks approach. We show how networks of Gaussian probabilistic bits or g-bits can be built out of networks of binary probabilistic bits (p-bit) where $N$ p-bits can represent $2N$ Gaussian states. Our setup is a heterogeneous probabilistic computer combining 5 stochastic Magnetic Tunnel Junction (sMTJ) based p-bits with a digital Field Programmable Gate Array (FPGA). In this setup, the only source of stochasticity comes from the thermal fluctuations of in-plane sMTJ s, while the FPGA serves as a deterministic CMOS platform hosting the weights and deterministic activation functions. We first demonstrate the tunability of individual g-bits by controlling their mean and standard deviation, followed by creating networks of coupled g-bits that can solve mixed binary-continuous optimization problems. Projections based on large-scale 0–1 mixed integer programs indicate the sMTJ -based g-bits can achieve up to a 3-order of magnitude reduction in transistor count and 2-order of magnitude in energy consumption over digital implementations. Our results demonstrate a promising path for scalable, energy-efficient and high-performance probabilistic computers to solve practical real valued optimization and machine learning problems.