发表机构
Leiden University; Fraunhofer Heinrich Hertz Institute; Department of Physics and Astronomy; University of Waterloo; Vector Institute; Porsche Digital GmbH（莱顿大学; 弗劳恩霍夫海因里希·赫兹研究所; 物理与天文学系; 滑铁卢大学; 向量研究所; 保时捷数字有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究量子机器学习中参数化量子电路缩放行为，通过加一扰动技术等给出分析结果，经数值实验验证其双重下降现象，表明更深的参数化量子电路不一定性能下降，为实际量子机器学习带来谨慎乐观理由。
AI 中文摘要
量子机器学习中的一个核心挑战是理解参数化量子电路（PQCs）的缩放行为。特别是，随着可训练参数数量的增加，它们在未见数据上的性能如何变化仍不清楚。先前的工作已经为量子模型推导了形式上的泛化保证，但众所周知，许多这样的结果并不能完全表征实际中的泛化行为。在这项工作中，我们表明基于梯度的PQCs随着模型大小的增加可以在未见数据上表现出改进的性能，呈现出双重下降现象。这与传统观点中更大的模型导致泛化性能下降形成对比。我们通过利用加一扰动技术和随机矩阵的谱性质，提供了严格支持这种行为的分析结果。我们通过在多个数据集和训练集大小上对重新上传的PQCs进行数值实验来支持这些结果，始终观察到预测的双重下降行为。虽然在实际量子机器学习的道路上仍然存在其他障碍，但我们发现更深的参数化量子电路不一定表现出性能下降，这为谨慎乐观提供了理由。
英文摘要
A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.
Comments21 pages (6+15), 2 figures (1+1), comments welcome
