Constructing Dynamical Systems to Model Higher Order Ising Spin Interactions and their Application in Solving Combinatorial Optimization Problems

TL;DR

This paper introduces dynamical systems that incorporate higher order interactions among Ising spins, enabling direct modeling and solving of complex combinatorial optimization problems involving hypergraph interactions.

Contribution

It presents novel dynamical models for higher order Ising interactions, extending beyond quadratic terms, to solve complex COPs like NAE-K-SAT and Max-K-Cut on hypergraphs.

Findings

Successfully modeled higher order Ising interactions

Solved NAE-K-SAT with K > 3 using the proposed system

Applied to Max-K-Cut on hypergraphs

Abstract

The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, the Ising model, and consequently, the corresponding dynamical system-based computational models primarily consider quadratic interactions among the nodes. Computational models considering higher order interactions among Ising spins remain largely unexplored. Therefore, in this work, we propose dynamical-system-based computational models to consider higher order (>2) interactions among the Ising spins, which subsequently, enables us to propose computational models to directly solve many COPs that entail such higher order interactions (COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K is greater than 3) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired 'toolbox' for solving COPs.