Quantum-Optimized Probabilistic U-Net with Quantum Entropy Calibration and Active Annotation for Reliable Sparse-Label MRI Brain Lesion Segmentations

Accurate and trustworthy segmentation of brain lesions in multimodal MRI is crucial for clinical decisions, yet most datasets carry only sparse voxel-level annotations. Conventional probabilistic U-Nets and classical uncertainty calibration struggle in this regime, often underestimating epistemic uncertainty and failing to preserve fine-grained topology or cross-scanner consistency sets. To overcome these limits, we present a Quantum-Optimized Probabilistic U-Net (Q-PUNet) equipped with a suite of quantum Inspired modules that address the main failure points of current practice sets. At its core, Quantum Entropy-Guided Uncertainty Calibration (QE-UC) embeds features into a Hilbert space and minimizes the Kullback–Leibler divergence between von Neumann entropy and Monte Carlo variance, refining confidence maps when labels are scarce. To reduce the cost of expert supervision, a Variational Quantum Active Annotation Loop (VQ-AAL) scores voxel importance via quantum Fisher information and queries only the most informative regions, lowering annotation workload by roughly 40 % without sacrificing Dice accuracy. Structural reliability is reinforced through Quantum Mutual Information Consistency Validation (Q-MICV), which encodes adjacent slices as quantum states and penalizes inter-slice mutual Information mismatches, improving 3-D coherence. For multi-center data, Hybrid Quantum–Classical Adversarial Domain Harmonization (HQADH) combines quantum kernel mapping with an adversarial discriminator to suppress scanner-specific artifacts, while Quantum Inspired Topological Persistence Regularization (Q-TPR) leverages quantum annealing of persistent homology to maintain correct Betti numbers and lesion topology sets. This integrated design raises expected Dice scores from 0.84 to about 0.89, cuts calibration error by up to 25 %, and improves cross-site generalization and topological fidelity. The framework delivers a practical route toward reliable, annotation-efficient, and clinically robust MRI lesion segmentations.