A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learning

Abstract:Quantum noise is expected to degrade quantum machine learning by driving circuits away from their noiseless implementations. Yet recent studies show moderate noise can reduce testing error, a behavior unexplained by weak-noise perturbative error accumulation or strong-noise trainability collapse. Here we develop a statistical learning theory connecting microscopic noise processes to macroscopic learning performance. At its heart is a noise-order purity parameter, derived from a surrogate model analysis, that predicts the noise-induced reduction in model complexity and the consequent reduction in the generalization gap. Noise simultaneously increases prediction bias. Their competition explains the intermediate-noise regime left open between these limits. It produces a finite-noise optimum whose location depends on the learning setup and can disappear in the large-sample limit. Numerical experiments validate these predictions. Noise programming can move a model towards this optimum. These results make the non-monotonic effect of noise predictable and provide a route to harness it.

Quantum Physics (quant-ph); Machine Learning (cs.LG)

arXiv:2608.24229 [quant-ph]

(or arXiv:2608.24229v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.24229 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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