Physics-Informed Machine Learning Correction of Variational Quantum Eigensolver Energies for Molecular Ground States

Abstract The variational quantum Eigensolver (VQE) provides a scalable route to molecular ground-state energies on near-term quantum hardware, but its accuracy degrades rapidly as system size grows because hardware-efficient ansätze cannot span the full correlation subspace. We introduce a physics-informed ridge regression correction that is trained on the difference between VQE and Hartree–Fock (HF) energies and applied as a postprocessing step requiring no additional quantum resources. The feature set─the VQE–HF energy gap ΔE, its square ΔE2, the active-space qubit count, the number of active electrons, and two cross-term interactions─captures the dominant drivers of ansatz error in a low-dimensional, interpretable form. The model is benchmarked on H2, H2O, NH3, CH4, C2H6, and CH3OH using the STO-3G basis set and a state vector VQE simulator using a two-layer Ry-CNOT hardware-efficient ansatz. To assess cross-molecule generalizability, the corrected framework is further tested on CO2, N2, and HCN under both untrained and trained conditions. Absolute energy errors fall from a range of 0.02–0.79 Ha (raw VQE) to 0.0007–0.094 Ha after correction, corresponding to improvement factors of 3× to 640× relative to CASCI reference values. Zero-shot generalization tests yield factors of 9–58×, and including molecules in training improves results by a further order of magnitude in several cases. The three extended molecules exhibit improvement factors of 4–6× in untrained settings and 5–6× after training, providing preliminary evidence of transferability across chemically distinct systems. These findings suggest that the VQE–HF energy gap encodes physically transferable information about correlation-energy saturation, and that even the smallest training set can produce practically useful corrections for near-term quantum chemistry.