Variational Quantum Regression for Binding Affinity Prediction: A Hybrid Quantum-Classical Framework with Explainable Molecular Descriptors

Predicting drug-target binding affinity with limited training data remains a central challenge in computational drug discovery. We introduce a hybrid quantum-classical framework combining molecular descriptors with variational quantum circuits for interpretable binding affinity prediction. Seven physicochemical descriptors (MW, logP, TPSA, HBD/HBA, rotatable bonds, aromatic rings) were encoded into 6-qubit variational circuits using parameterized rotations and controlled-Z entanglement. Quantum kernels were extracted and used for regression on 1,200 BindingDB molecules across kinase, GPCR, and protease targets, with external validation on 300 ChEMBL compounds. Performance was compared against SVR, random forest, gradient boosting, and neural network baselines using 100-fold bootstrap validation. Variational quantum regression achieved MSE = 0.056 ± 0.009, outperforming SVR by 32% (0.082 ± 0.013), RF by 28%, and GBM by 24%. Quantum advantage was most significant in low-data regimes (n 0.85 versus R2 < 0.72 for classical methods. External validation confirmed generalization (R2 = 0.83). Our Explainable Quantum Pharmacology framework revealed TPSA and logP as dominant predictive features through gradientbased sensitivity analysis, aligning with established medicinal chemistry principles. Quantum kernels provide measurable, chemically interpretable improvements for molecular property prediction in data-limited scenarios. This work demonstrates practical quantum advantage for early-stage drug discovery applications on near-term quantum hardware.