$i$Trust: Trust-Region Optimisation with Ising Machines

TL;DR

This paper introduces a novel application of Ising machines for trust-region optimization with box constraints, demonstrating convergence and potential for classical and quantum hybrid applications.

Contribution

It proposes modifications to opto-electronic oscillator-based Ising machines enabling trust-region optimization with proven convergence under convexity assumptions.

Findings

Modified Ising machine converges under convexity or invexity.

New trust-region method effectively solves unconstrained problems.

Analytical proof of convergence supports practical feasibility.

Abstract

In this work, we present a heretofore unseen application of Ising machines to perform trust region-based optimisation with box constraints. This is done by considering a specific form of opto-electronic oscillator-based coherent Ising machines with clipped transfer functions, and proposing appropriate modifications to facilitate trust-region optimisation. The enhancements include the inclusion of non-symmetric coupling and linear terms, modulation of noise, and compatibility with convex-projections to improve its convergence. The convergence of the modified Ising machine has been shown under the reasonable assumptions of convexity or invexity. The mathematical structures of the modified Ising machine and trust-region methods have been exploited to design a new trust-region method to effectively solve unconstrained optimisation problems in many scenarios, such as machine learning and optimisation of parameters in variational quantum algorithms. Hence, the proposition is useful for both classical and quantum-classical hybrid scenarios. Finally, the convergence of the Ising machine-based trust-region method, has also been proven analytically, establishing the feasibility of the technique.