SLT: Robust Quantum Neural Networks for Noisy-Label Medical Image Classification via Supermartingale-based Label Transition

Noisy-label learning in small-scale medical image classification remains challenging, as limited data can amplify annotation errors. While quantum neural networks (QNNs) have recently been explored as compact models for small-data regimes, their behavior under label corruption remains insufficiently understood. A key obstacle is QNNs' intrinsic "natural smoothness", which may regularize training but also obscure high-confidence samples needed for noise-transition estimation. We propose Supermartingale-based Label Transition (SLT), an anchor-free loss correction framework for robust QNN-based medical image classification under noisy labels. SLT models entropy reduction in predictive distributions as a supermartingale and uses its monotonic behavior to identify stable transition-matrix refinement steps. This enables dynamic transition updates while reducing noise-driven oscillations during QNN training. We further provide a convergence analysis showing that the proposed transition-refinement process reaches a steady state. Experiments on multiple public small-scale medical image datasets demonstrate that SLT improves QNN-based noisy-label classification and outperforms classic noisy-label learning baselines under synthetic and real-world label noise.