Quantum machine learning for predicting properties of van der Waals bilayers.

Layering two-dimensional (2D) materials into van der Waals bilayers provides an effective method to achieve innovative quantum states and tunable electronic properties. Exploring the extensive configurational space resulting from various layer combinations, twist angles, and stacking patterns presents a significant computing challenge. As the volume of accessible datasets expands, training machine learning models on conventional hardware may ultimately become excessively expensive, prompting the advancement of quantum machine learning (QML) methodologies for materials discovery. This study presents a quantum-enhanced machine learning framework for predicting the bandgaps of van der Waals bilayers utilizing quantum simulators. We start with conventional feature selection to ascertain the most important descriptors affecting electronic properties. The properties are subsequently encoded into quantum states utilizing parameterized quantum circuits. We evaluated three quantum feature maps, namely ZFeatureMap, ZZFeatureMap, and PauliFeatureMap, and observed task-dependent performance. For the classification task, ZFeatureMap with two repetitions gave the strongest quantum-classifier performance, whereas for Quantum Support Vector Regressor (QSVR) bandgap regression, PauliFeatureMap with one repetition achieved the lowest average root-mean-square error (RMSE). These results indicate that feature-map choice should be optimized separately for classification and regression rather than being interpreted as the universal superiority of a single feature map. Using these feature-map comparisons, we employ a QSVR and a variational quantum regressor to predict the bandgaps of 1850 semiconducting vdW bilayers, illustrating that QML may attain significant predictive accuracy despite limited training data. Overall, the results demonstrate the feasibility of a simulator-based QML workflow for materials-property prediction. The quantum classifiers are competitive with the classical support vector classifier (SVC) baseline for zero-gap/non-zero-gap classification, whereas the classical Support Vector Regression (SVR) achieves the lowest RMSE in the regression task. Therefore, the present study should be interpreted as an exploratory benchmark of hybrid classical-quantum models for van der Waals (vdW) bilayers rather than as evidence of a definitive quantum performance advantage.