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

Mohammad Hizzani, Arne Heittmann, George Higgins Hutchinson, Dmitrii Dobrynin, Thomas Van Vaerenbergh, Tinish Bhattacharya, Adrien Renaudineau, Dmitri B. Strukov, John Paul Strachan

Abstract: Ising solvers offer a promising physics-based approach to tackle the challenging class of combinatorial optimization problems. However, typical solvers operate in a quadratic energy space, having only pair-wise coupling elements which already dominate area and energy. We show that such quadratization can cause severe problems: increased dimensionality, a rugged search landscape, and misalignment with the original objective function. Here, we design and quantify a higher-order Hopfield optimization solver, with 28nm CMOS technology and memristive couplings for lower area and energy computations. We combine algorithmic and circuit analysis to show quantitative advantages over quadratic Ising Machines (IM)s, yielding 48x and 72x reduction in time-to-solution (TTS) and energy-to-solution (ETS) respectively for Boolean satisfiability problems of 150 variables, with favorable scaling.