  This study investigates the application of Factorization Machines with
Quantum Annealing (FMQA) to address the crystal structure problem (CSP) in
materials science. FMQA is a black-box optimization algorithm that combines
machine learning with annealing machines to find samples to a black-box
function that minimize a given loss. The CSP involves determining the optimal
arrangement of atoms in a material based on its chemical composition, a
critical challenge in materials science. We explore FMQA's ability to
efficiently sample optimal crystal configurations by setting the loss function
to the energy of the crystal configuration as given by a predefined interatomic
potential. Further we investigate how well the energies of the various
metastable configurations, or local minima of the potential, are learned by the
algorithm. Our investigation reveals FMQA's potential in quick ground state
sampling and in recovering relational order between local minima.
