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Ising solvers offer a promising physics-based approach to tackle thechallenging class of combinatorial optimization problems. However, typicalsolvers operate in a quadratic energy space, having only pair-wise couplingelements which already dominate area and energy. We show that suchquadratization can cause severe problems: increased dimensionality, a ruggedsearch landscape, and misalignment with the original objective function. Here,we design and quantify a higher-order Hopfield optimization solver, with 28nmCMOS technology and memristive couplings for lower area and energycomputations. We combine algorithmic and circuit analysis to show quantitativeadvantages over quadratic Ising Machines (IM)s, yielding 48x and 72x reductionin time-to-solution (TTS) and energy-to-solution (ETS) respectively for Booleansatisfiability problems of 150 variables, with favorable scaling.

Memristor-based hardware and algorithms for higher-order Hopfield optimization solver outperforming quadratic Ising machines