QStruct: Quantum-Circuit Structural Priors for Data-Efficient Molecular Representation Learning

Reliable molecular prediction under scarce labels and chemical distribution shift benefits from structural biases beyond local geometry. We introduce QStruct, a hybrid framework in which a pooled geometric GNN embedding sets bounded rotation angles for a shallow eight-qubit ring circuit. Eight single-qubit $Z$ expectations and seven adjacent $ZZ$ correlations form a 15-dimensional feature vector fused with the graph representation. Exact classical state-vector evaluation supplies this inductive bias without claiming quantum advantage. Across QM9, MD17, PCQM4Mv2, and OC20, reported results support data efficiency and extrapolation while retaining competitive full-data accuracy. With 100 QM9 training molecules, MAE is $0.059$, versus $0.070$–$0.074$ for strong baselines; full-data OC20 OOD-Adsorbate/Catalyst errors decrease from $0.58/0.62$ to $0.54/0.59$. Controlled ablations favor learned circuit features over frozen or classical alternatives, while coverage curves reveal remaining calibration gaps. Separate descriptive records illustrate uncertainty ranking, computational trade-offs, and target-dependent residuals without adding independently verified benchmark evidence. Code: https://anonymous.4open.science/r/QCMRL-7203.