对比量子启发编码在经典数据上的表现,发现其优势不显著。
A Matched Spectral Benchmark of Quantum Inspired Feature Maps
- 用匹配维度的固定编码方法比较幅度、角度和基底编码
- 三种编码均未超越线性模型或随机傅里叶特征,性能平庸
- 适合关注量子机器学习机制原理的研究者
量子机器学习常声称量子系统能揭示经典模型难以捕捉的高维结构。本文聚焦于数据编码映射这一核心组件,评估幅度、角度和基底编码作为经典监督学习中的确定性特征映射,在匹配输出维度和强经典控制下的表现。基准测试覆盖多样经典数据集,对比了原始线性模型、随机傅里叶特征、多项式特征、PCA、RBF SVM 和浅层神经网络。不将性能视为单一终点,而是通过有效秩、条件数、中心核对齐、预测性能和实际开销分析每种表示的几何特性。结果表明:幅度编码经单位球归一化会丢失幅度信息;角度编码在几何上与原始线性特征冗余;基底编码引入二元汉明几何,与光滑决策结构对齐不佳。这些发现并不否定量子计算,但表明仅靠固定的量子启发编码几何,并不能为经典数据提供可靠的机器学习优势。
原文摘要 · Abstract (English)
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed data-encoding map. Amplitude, angle, and basis encoding are evaluated as deterministic feature maps for classical supervised learning under matched output dimensionality and strong classical controls. The benchmark compares these encodings against raw linear models, random Fourier features, polynomial features, PCA, RBF SVMs, and shallow neural networks across diverse classical datasets. Rather than treating performance as a single endpoint, we analyze the geometry of each representation through effective rank, condition number, centered kernel alignment, predictive performance, and practical overhead. The resulting picture is mechanistic: amplitude encoding can remove magnitude information through unit-sphere normalization, angle encoding can become geometrically redundant with raw linear features, and basis encoding can impose a binary Hamming geometry that is poorly aligned with smooth decision structure. These findings do not argue against quantum computation, however, they show that fixed quantum-inspired encoding geometry alone is not a reliable source of machine-learning advantage on classical data.
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