Efficient Optimization with Higher-Order Ising Machines

TL;DR

This paper demonstrates that higher-order Ising machines, implemented with coupled oscillators, can solve satisfiability problems more efficiently and effectively than traditional second-order Ising machines, advancing the state-of-the-art in optimization hardware.

Contribution

It introduces higher-order Ising machines for satisfiability problems, showing they are more resource-efficient and yield better solutions than second-order Ising machines.

Findings

Higher-order Ising machines use fewer spins and connections.

They solve Boolean satisfiability problems more efficiently.

They outperform second-order Ising machines on benchmark datasets.

Abstract

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order interactions although important classes of optimization problems, such as satisfiability problems, map more seamlessly to Ising networks with higher-order interactions. Here, we demonstrate that higher-order Ising machines can solve satisfiability problems more resource-efficiently in terms of the number of spin variables and their connections when compared to traditional second-order Ising machines. Further, our results show on a benchmark dataset of Boolean \textit{k}-satisfiability problems that higher-order Ising machines implemented with coupled oscillators rapidly find solutions that are better than second-order Ising machines, thus, improving the current state-of-the-art for Ising machines.