This paper is a contribution to the Physical Review Applied collection titled Physics-Inspired Computing.

Many hard combinatorial problems can be mapped onto Ising models, which replicate the behavior of classical spins. Recent advances in probabilistic computers are characterized by parallelization and the introduction of novel hardware platforms. An interesting application of probabilistic computers is to operate them in “reverse” mode, where the network self-organizes its behavior to find the input bits that result in an output state. This can be used, for example, as a factorizer of semiprimes. One issue with simulating probabilistic computers on standard logic devices, such as field-programmable gate arrays, is that the update rules for each spin involve many multiplications, evaluation of a hyperbolic tangent, and a high-resolution numerical comparison. We simplify these rules, which improves the spatial and temporal circuit complexity when simulating a probabilistic computer on a field-programmable gate array. Applying our method to factorizing semiprimes, we achieve at least an order-of-magnitude reduction in the on-chip resources and the time to solution compared to recently reported methods. For a 32-bit semiprime, we achieve an average factorization in $\sim 100$ s. Our approach will inspire new physical realizations of probabilistic computers because we relax some of their update-rule requirements.

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• Dynamics of networks
• Optimization problems
• Probabilistic computing
• Self-organized systems
• Devices for digital logic, storage & processing
• Combinatorics
• Ising model
• Thermal & statistical models