提出谱相位编码,提升量子核方法在噪声下的稳定性。
Spectral Phase Encoding for Quantum Kernel Methods
- 用离散傅里叶变换结合相位嵌入,实现结构对齐的量子特征编码。
- 在多种真实数据集上,相比PCA和随机投影,噪声增加时性能下降最慢。
- 适合关注量子机器学习鲁棒性的研究者,尤其在近中期量子硬件场景下。
量子核方法在近期量子机器学习中前景广阔,但其在数据污染下的表现尚不明确。本文分析了受控加性噪声下量子特征构造的退化行为。提出谱相位编码(SPE),一种结合离散傅里叶变换(DFT)前端与对角相位嵌入的混合构造,该嵌入与对角量子映射几何一致。在统一框架下,比较了基于DFT的量子核(QK-DFT)与其它量子变体(QK-PCA、QK-RP)及经典SVM基线,在相同清洁数据超参数选择下的表现,通过数据集固定效应回归与野集群聚自举推断量化鲁棒性。在量子家族中,基于DFT的预处理在噪声增加时表现出最小的退化率,与PCA和RP相比具有统计显著的斜率差异。相较于经典基线,QK-DFT的退化程度接近线性SVM,且优于RBF SVM在匹配调优下的稳定性。硬件实验表明,SPE在重叠估计任务中仍可执行且数值稳定。结果表明,量子核的鲁棒性关键取决于结构对齐的预处理及其与对角嵌入的交互作用,支持在近似量子时代采用鲁棒性优先的设计思路。
原文摘要 · Abstract (English)
Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive noise. We introduce Spectral Phase Encoding (SPE), a hybrid construc- tion combining a discrete Fourier transform (DFT) front-end with a diagonal phase-only embedding aligned with the geometry of diagonal quantum maps. Within a unified framework, we compare QK-DFT against alternative quantum variants (QK-PCA, QK-RP) and classi- cal SVM baselines under identical clean-data hyperparameter selection, quantifying robustness via dataset fixed-effects regression with wild cluster bootstrap inference across heterogeneous real-world datasets. Across the quantum family, DFT-based preprocessing yields the smallest degradation rate as noise increases, with statistically sup- ported slope differences relative to PCA and RP. Compared to classical baselines, QK-DFT shows degradation comparable to linear SVM and more stable than RBF SVM under matched tuning. Hardware exper- iments confirm that SPE remains executable and numerically stable for overlap estimation. These results indicate that robustness in quan- tum kernels depends critically on structure-aligned preprocessing and its interaction with diagonal embeddings, supporting a robustness-first perspective for NISQ-era quantum machine learning.
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