Quantum U-Net with Uncertainty Quantification for Brain Tumor Segmentation: A Hybrid Quantum-Classical Approach

Precise segmentation of brain tumors from multi-modal magnetic resonance imaging (MRI) scans remains a challenging requirement for clinical diagnosis and treatment planning. This paper introduces a hybrid quantum-classical architecture that places a six-qubit variational quantum circuit (VQC) inside a 3D U-Net encoder-decoder. Rather than replacing the entire bottleneck, the VQC operates as a squeeze-and-excitation style channel attention block: global-average-pooled channel descriptors are angle-encoded into qubits, passed through two Strongly Entangling Layers, and the resulting measurements are applied as multiplicative channel weights. This noisy intermediate-scale quantum (NISQ)-compatible design uses only two layers and 36 parameters, so the quantum overhead per forward pass is confined to a single channel vector. For uncertainty estimation, we combine Monte Carlo Dropout entropy with quantum measurement variance to produce per-voxel confidence maps. Evaluated on Brain Tumor Segmentation 2020 with nine model variants, with test-time augmentation and adaptive thresholding, the proposed architecture reaches a mean Dice of 0.7812, HD95 of 23.87 (necrotic/non-enhancing core), 2.46 (ED), and 10.47 (ET), and an expected calibration error (ECE) of 0.0655—matching the strongest classical baseline on Dice while cutting ECE by roughly 20%. All stable quantum variants outperform their classical counterparts in calibration, confirming that quantum measurement stochasticity provides an additional, complementary uncertainty signal beyond dropout alone.