Analysis of Higher-Order Ising Hamiltonians

TL;DR

This paper introduces IsingSim, a theoretical framework for simulating higher-order Ising models efficiently, enabling better design and understanding of complex Ising machines for industrial applications.

Contribution

It presents a novel, self-customizable simulation framework that decouples Ising spins and gradients, significantly accelerating higher-order Ising model simulations.

Findings

Accelerated simulation speed via bidirectional approach

Verified framework with exact and approximate gradients

Provides design guidelines for higher-order Ising machines

Abstract

It is challenging to scale Ising machines for industrial-level problems due to algorithm or hardware limitations. Although higher-order Ising models provide a more compact encoding, they are, however, hard to physically implement. This work proposes a theoretical framework of a higher-order Ising simulator, IsingSim. The Ising spins and gradients in IsingSim are decoupled and self-customizable. We significantly accelerate the simulation speed via a bidirectional approach for differentiating the hyperedge functions. Our proof-of-concept implementation verifies the theoretical framework by simulating the Ising spins with exact and approximate gradients. Experiment results show that our novel framework can be a useful tool for providing design guidelines for higher-order Ising machines.