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

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 ΔE ², 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.