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 principled 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.