通过多阶段残差学习缓解量子模型的频率偏见问题。
Mitigating Frequency Learning Bias in Quantum Models via Multi-Stage Residual Learning
- 采用多阶段残差训练，逐轮优化高频和非主导频率成分。
- 在合成数据集上，残差学习使测试均方误差显著降低。
- 适用于需要高阶频谱表达能力的量子机器学习任务。
基于参数化量子线路的量子机器学习模型可视为傅里叶级数逼近器。然而，它们通常难以学习具有多个频率分量的函数，尤其是高频或非主导频率分量；我们称此现象为量子傅里叶参数化偏见。受经典傅里叶神经算子（FNOs）的启发，我们将多阶段残差学习思想引入量子领域，通过迭代训练额外的量子模块来拟合前一阶段的残差。我们在一个合成基准上进行评估，该基准包含空间局部化的不同包络形状（高斯、洛伦兹、三角形）的频率成分。系统性实验表明，量子比特数量、编码方案以及残差学习均对解析多频率至关重要；仅使用残差学习即可在相同总训练周期下显著优于单阶段基线。本工作提供了一个提升量子模型频谱表达能力的实际框架，并揭示了其频率学习行为的新见解。
原文摘要 · Abstract (English)
Quantum machine learning models based on parameterized circuits can be viewed as Fourier series approximators. However, they often struggle to learn functions with multiple frequency components, particularly high-frequency or non-dominant ones; a phenomenon we term the quantum Fourier parameterization bias. Inspired by recent advances in classical Fourier neural operators (FNOs), we adapt the multi-stage residual learning idea to the quantum domain, iteratively training additional quantum modules on the residuals of previous stages. We evaluate our method on a synthetic benchmark composed of spatially localized frequency components with diverse envelope shapes (Gaussian, Lorentzian, triangular). Systematic experiments show that the number of qubits, the encoding scheme, and residual learning are all crucial for resolving multiple frequencies; residual learning alone can improve test MSE significantly over a single-stage baseline trained for the same total number of epochs. Our work provides a practical framework for enhancing the spectral expressivity of quantum models and offers new insights into their frequency-learning behavior.
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