Abstract
We formalize an inverse, data-conditioned variant of the Variational Quantum Eigensolver (VQE) for clinical biomarker discovery. Given patient-encoded quantum states, we construct a task-specific Hamiltonian whose coefficients are inferred from clinical associations and interpret its expectation value as a calibrated energy score for prognosis and treatment monitoring. The method integrates coefficient estimation, ansatz specification with basis rotations, commuting-group measurements, and a practical shot budget analysis. Evaluated on public infectious disease datasets under severe class imbalance, the approach yields consistent gains in balanced accuracy and precision–recall over strong classical baselines, with stability across random seeds and feature ablations. This variational energy scoring framework bridges Hamiltonian learning and clinical risk modeling, offering a compact, interpretable, and reproducible route to biomarker prioritization and decision support.