Continuous Approximation of the Ising Hamiltonian: Exact Ground States and Applications to Fidelity Assessment in Ising Machines

TL;DR

This paper introduces a continuous approximation method for solving large-scale Ising problems, providing exact solutions for certain models and enabling fidelity assessment of Ising machines through comparison with analytical results.

Contribution

The authors develop a novel continuous reformulation of the Ising Hamiltonian that yields exact solutions for specific models, aiding in benchmarking Ising machine performance.

Findings

Quantum-inspired algorithms match analytical solutions

Quantum Ising machine shows deviations from exact solutions

Method enables analytical solutions for complex Ising problems

Abstract

In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a non-trivial class of fully connected Ising models. To validate our method, we conducted numerical experiments comparing our analytical solutions with those obtained from a quantum-inspired Ising algorithm and a quantum Ising machine. The results demonstrate that the quantum-inspired algorithm and brute-force method successfully align with our solutions, while the quantum Ising machine exhibits notable deviations. Our method offers promising avenues for analytically solving diverse Ising problem instances, while the class of Ising problems addressed here provides a robust framework for assessing the fidelity of Ising machines.