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

• URL: http://arxiv.org/abs/2608.24229v1
• Date: Tue, 25 Aug 2026 08:32:46 GMT
• Title: A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learning
• Abstract summary: Quantum noise is expected to degrade quantum machine learning by driving circuits away from their noiseless implementations.<n>Yet recent studies show moderate noise can reduce testing error, a behavior unexplained by weak-noise perturbative error accumulation or strong-noise trainability collapse.<n>Here we develop a statistical learning theory connecting microscopic noise processes to macroscopic learning performance.
• Score: 5.083987940956758
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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