How Noisy Training Reduces Model Discrepancy in Quantum Machine Unlearning

Machine unlearning aims to remove the influence of selected training data without retraining from scratch. While calibrated training noise can support unlearning guarantees in classical learning, native noise in quantum neural networks (QNNs) is not designed for this purpose. We study how native quantum noise affects the pre-to-post discrepancy between the original (pre-unlearn) model distribution and its retrained gold-standard reference under the same noise regime, before any unlearning update is applied. We develop a trajectory-level 2-Wasserstein analysis that decomposes this discrepancy into deletion-induced update differences, their subsequent propagation, and finite-shot gradient fluctuations. For exact-expectation readout noise, this analysis yields explicit channel-dependent bounds and identifies conditions under which their geometric envelopes become smaller than the noiseless counterpart. We further construct a fixed-QNN example showing that arbitrarily small Wasserstein discrepancy can coexist with maximal deletion sensitivity. Experiments on a 4-qubit QNN show discrepancy reductions in selected readout and interleaved channel regimes, while finite-shot measurement provides no comparable reduction in the tested settings. A 10-qubit MNIST study additionally shows that selected noise regimes reduce unlearning optimization costs. Together, these findings suggest that native quantum noise can facilitate unlearning in selected regimes, while distinguishing geometric proximity and optimization savings from certified removal of data influence.