arXiv:2607.21409quant-phcs.LG2026-07

发现量子电路越大越能泛化,挑战了传统认知。

Cautious optimism for deep parameterized quantum circuits

  • 用随机矩阵谱分析和扰动技术解析量子电路泛化机制。
  • 实验证明参数增多时预测误差先降后升,出现双下降现象。
  • 适合关注量子机器学习模型设计的研究者参考。

量子机器学习的核心挑战之一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增加,其在未见数据上的性能如何变化仍不明确。以往工作虽推导出量子模型的泛化保证,但这些理论结果往往无法充分刻画实际中的泛化表现。本文表明,基于梯度的PQC在模型规模增大时,对未见数据的性能反而提升,呈现出双下降现象,这与传统认为大模型会劣化泛化的观点相悖。我们通过加一扰动技术和随机矩阵的谱性质,严格推导出该行为的解析依据。数值实验在多个数据集和不同训练集大小下,对重加载型PQC进行测试,一致观测到预期的双下降趋势。尽管实现实用量子机器学习仍有诸多障碍,但本研究发现更深的参数化量子电路未必导致性能退化,为该领域带来谨慎乐观的前景。

原文摘要 · Abstract (English)

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.

量子机器学习双下降泛化分析

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