发表机构
University of Washington; University of Michigan（华盛顿大学; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建统计学习理论，揭示量子噪声的非单调效应，推导噪声阶纯度参数解释中间噪声 regime，数值实验验证其预测，表明适度噪声可降低泛化误差，提供利用噪声的途径。
AI 中文摘要
量子噪声预计会通过使量子电路偏离无噪声实现而降低量子机器学习的性能，但近期研究表明适度噪声可降低测试误差，这种行为无法用弱噪声微扰误差累积或强噪声可训练性崩溃解释。本文构建了将微观噪声过程与宏观学习性能关联的统计学习理论，核心是从代理模型分析推导得到的噪声阶纯度参数，该参数可预测噪声诱导的模型复杂度降低及由此产生的泛化 gap 减小；噪声同时会增加预测偏差，二者的竞争关系解释了介于弱、强噪声极限之间的中间噪声 regime，产生的有限噪声最优值位置依赖于学习设置，在大样本极限下可能消失。数值实验验证了这些预测，噪声编程可将模型推向该最优值，这些结果使噪声的非单调效应可预测，并提供了利用该效应的途径。
英文摘要
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.
Comments36 pages, 11 figures
