Several hundred plasma-assisted molecular beam epitaxy synthesis experiments of GaN and ZnO thin film crystals were organized into data sets that correlate the operating parameters selected for growth to two figures of merit: a binary determination of surface morphology, and a continuous Bragg–Williams measure of lattice ordering (S2). Quantum as well as conventional supervised machine learning algorithms were optimized and trained on the data, enabling a comparison of their generalization performance. The models displaying the best generalization performance on each data set were subsequently used to predict each figure of merit across the ZnO and GaN processing spaces.