  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.
