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Autonomous materials science, where active learning is used to navigate large compositional phase space, has emerged as a powerful vehicle to rapidly explore new materials. A crucial aspect of autonomous materials science is exploring new materials using as little data as possible. Gaussian process-based active learning allows effective charting of multi-dimensional parameter space with a limited number of training data and, thus, is a common algorithmic choice for autonomous materials science. An integral part of the autonomous workflow is the application of kernel functions for quantifying similarities among measured data points. A recent theoretical breakthrough has shown that quantum kernel models can achieve similar performance with less training data than classical kernel models. This signals the possible advantage of applying quantum kernel machine learning to autonomous materials discovery. In this work, we compare quantum and classical kernels for their utility in sequential phase space navigation for autonomous materials science. In particular, we compute a quantum kernel and several classical kernels for x-ray diffraction patterns taken from an Fe–Ga–Pd ternary composition spread library. We conduct our study on both IonQ’s Aria trapped ion quantum computer hardware and the corresponding classical noisy simulator. We experimentally verify that a quantum kernel model can outperform some classical kernel models. The results highlight the potential of quantum kernel machine learning methods for accelerating materials discovery and suggest that complex x-ray diffraction data are a candidate for robust quantum kernel model advantage.