Disentangling Noise and Epistemic Uncertainty in Quantum Machine Learning

Uncertainty quantification (UQ) is essential for reliable quantum machine learning (QML), but on near-term hardware epistemic uncertainty is entangled with finite-shot measurement noise and device noise. We study variational quantum circuits with additive Gaussian perturbations of rotation angles and show that this perturbation model induces structured random-unitary channels, admits a variational-Bayesian interpretation, and yields a local Gaussian-process approximation under linearization. Our main statistical result proves that epistemic variance is identifiable only when sampling is performed across parameter configurations rather than across shots. This motivates hierarchical $M\times S$ sampling schemes that improve predictive mean and variance estimation at fixed shot budget. Simulations and proof-of-concept experiments on IQM Garnet are performed to validate assumptions of the theoretical results and as an additional empirical proof-of-concept that the proposed sampling schemes recovers predictive uncertainty more efficiently than naive shot scaling in the studied regimes.