Machine Learning Framework for Quantum Sampling of Highly-Constrained, Continuous Optimization Problems

TL;DR

This paper introduces a machine learning framework that maps continuous inverse design problems into QUBO formulations, enabling the use of quantum and classical samplers to find superior designs in science and engineering.

Contribution

The work presents a novel ML-based approach combining variational autoencoders and factorization machines to solve inverse design problems via quantum sampling, outperforming training set figures of merit.

Findings

Framework finds designs exceeding training set performance.

Demonstrated on thermal emitter and diffractive grating problems.

Uses hybrid quantum-classical samplers for optimization.

Abstract

In recent years, there is a growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design problems into surrogate quadratic unconstrained binary optimization (QUBO) problems by employing a binary variational autoencoder and a factorization machine. The factorization machine is trained as a low-dimensional, binary surrogate model for the continuous design space and sampled using various QUBO samplers. Using the D-Wave Advantage hybrid sampler and simulated annealing, we demonstrate that by repeated resampling and retraining of the factorization machine, our framework finds designs that exhibit figures of merit exceeding those of its training set. We showcase the framework's performance on two inverse design problems by optimizing (i) thermal emitter topologies for thermophotovoltaic applications and (ii) diffractive meta-gratings for highly efficient beam steering. This technique can be further scaled to leverage future developments in quantum optimization to solve advanced inverse design problems for science and engineering applications.