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

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.