Quantum Kernel Regression and Variational Quantum Regression for the CCS Prediction of Dissolved Organic Matter: A...

Recent advances in quantum machine learning (QML) offer new opportunities for chemical property prediction, yet their practical performance relative to established classical models remains poorly characterized on real-world datasets. Building on our previous benchmark of classical and deep learning models for collision cross-section (CCS) predictions, we present an empirical comparison of quantum kernel regression (QKR) and a variational quantum regressor (VQR) against classical machine learning (CML) techniques, including Random Forest (RF), support vector regression (SVR), Lasso, and a Voting Regressor (VR) ensemble. Using an aquatic dissolved organic matter (DOM) dataset with five molecular descriptors and five chemical classes, we systematically investigate QKR feature map repetitions and classical readout kernels, as well as VQR circuit depths and optimizer choices, to identify performance-optimal QML configurations. Regression performance is evaluated using the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2) across training-set sizes up to 600 molecules per class. Overall, RF and Lasso deliver the most robust CCS predictions, achieving R2 ≥ 0.9 for lignins, carbohydrates, lipids, and proteins. Meanwhile, the optimized QKR architecture exhibits substantial gains as data increase and achieves competitive performance on chemically homogeneous subsets such as carbohydrates and lipids. In contrast, the VQR ansatz remains consistently weaker than both QKR and the classical baselines across all classes and data sizes. The results highlight the strong influence of dataset size, feature representation, and molecular heterogeneity on QML performance while also identifying conditions under which quantum methods may become competitive in future studies.