Probabilistic Computing Optimization of Complex Spin-Glass Topologies

Spin glass systems as lattices of disordered magnets with random interactions have important implications within the theory of magnetization and applications to a wide-range of hard combinatorial optimization problems. Nevertheless, despite sustained efforts, algorithms that attain both high accuracy and efficiency remain elusive. Due to their topologies being low-$k$-partite such systems are well suited to a probabilistic computing (PC) approach using probabilistic bits (P-bits). Here we present complex spin glass topologies solved on a simulated PC realization of an Ising machine. First, we considered a number of three dimensional Edwards-Anderson cubic spin-glasses randomly generated as well as found in the literature as a benchmark. Second, biclique topologies were identified as a likely candidate for a comparative advantage compared to other state-of-the-art techniques, with a range of sizes simulated. We find that the number of iterations necessary to find solutions of a given quality has constant scaling with system size past a saturation point if one assumes perfect parallelization of the hardware. Therefore a PC architecture can trade the computational depth of other methods for parallelized width by connecting a number of P-bits that scales linearly in system size. This constant scaling is shown to persist across a number of solution qualities, up to a certain limit beyond which resource constraints limited further investigation. The saturation point varies between topologies and qualities and becomes exponentially hard in the limit of finding the ground truth. Furthermore we demonstrate that our PC architecture can solve spin-glass topologies to the same quality as the most advanced quantum annealer in minutes, making modest assumptions about their implementation on hardware.