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.

翻译：伊辛求解器为应对组合优化问题这一难题提供了富有前景的物理学方法。然而，典型求解器在二次能量空间中运行，仅具备成对耦合元件，而这些元件已占据主导面积与能耗。我们证明，此类二次化可能导致严重问题：维度增加、搜索空间崎岖不平，以及与原始目标函数失配。本文设计并量化了一种高阶Hopfield优化求解器，采用28nm CMOS技术与忆阻耦合实现更低面积与能耗计算。我们结合算法与电路分析，展示其相较于二次型伊辛机（IM）的定量优势：针对150变量的布尔可满足性问题，求解时间（TTS）与求解能耗（ETS）分别降低48倍与72倍，且具有良好扩展性。