Ising machines are a form of quantum-inspired processing-in-memory computer which has shown great promise for overcoming the limitations of traditional computing paradigms while operating at a fraction of the energy use. The process of designing Ising machines is known as the reverse Ising problem. Unfortunately, this problem is in general computationally intractable: it is a nonconvex mixed-integer linear programming problem which cannot be naively brute-forced except in the simplest cases due to exponential scaling of runtime with number of spins. We prove new theoretical results which allow us to reduce the search space to one with quadratic scaling. We utilize this theory to develop general purpose algorithmic solutions to the reverse Ising problem. In particular, we demonstrate Ising formulations of 3-bit and 4-bit integer multiplication which use fewer total spins than previously known methods by a factor of more than three. Our results increase the practicality of implementing such circuits on modern Ising hardware, where spins are at a premium.

翻译：伊辛机是一种受量子启发的存算一体计算机，在克服传统计算范式局限性的同时仅需极低能耗，展现出巨大潜力。伊辛机的设计过程被称为逆向伊辛问题。遗憾的是，该问题在一般情况下计算上难以处理：它是一个非凸混合整数线性规划问题，除最简单情形外，由于运行时间随自旋数呈指数级增长，无法通过穷举法求解。我们证明了新的理论成果，能够将搜索空间缩减至二次缩放规模。基于该理论，我们开发了逆向伊辛问题的通用算法解决方案。特别地，我们展示了3位和4位整数乘法的伊辛实现，其总自旋数较先前方法减少三倍以上。我们的研究成果推进了此类电路在现代伊辛硬件（自旋资源极为珍贵）上的实用化进程。