arXiv：cs.LG· Ana Paula Appel·· 5 小时前AI 评分33
分形维度可预测角度编码数据中的量子核坍缩
Fractal dimension predicts quantum kernel collapse in angle-encoded data
AI 导读
研究提出用相关分形维度 D2 作为角度编码量子核的先验量子比特预算，在九个数据集和态矢量模拟器（n=32）上，单层 ZZ 保真核在 q=D2 时保持几何存活，而 PCA-95% 宽度下已坍缩。
正文
Abstract:Angle-encoded quantum kernels on tabular data collapse when the feature map is wider than the intrinsic dimension of the data. We propose the correlation fractal dimension D2 as an a priori qubit budget: encode D2 coordinates chosen by FD-ASE instead of the PCA-95% width or all E attributes. On nine data sets and a statevector simulator (n= 32), a one-layer ZZ fidelity kernel at q=D2 stays geometrically alive while the same kernel at the PCA-95% width has already collapsed. The budget is map-dependent: product-state and IQP maps overshoot it; a second ZZ layer undershoots it. Packed dense-angle and re-uploading encodings still live at the fractal q, but not when PCA-95% features are stacked onto those qubits. Shrinking the angle bandwidth moves the ZZ knee later; stretching it kills the kernel earlier. On IBM Quantum (ibm_fez, 256 shots, n=8) the one-layer ZZ kernel at the fractal width matches the exact kernel (MAE 0.021); past that width both hardware and simulator have collapsed. The ceiling is a property of the map-data pair at a stated bandwidth, not of the classical table alone.
| Comments: | 28 pages, 12 figures. Submitted to Quantum Machine Intelligence |
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.00475 [quant-ph] |
| (or arXiv:2609.00475v2 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2609.00475 arXiv-issued DOI via DataCite |
Submission history
From: Ana Paula Appel [view email]
[v1]
Mon, 31 Aug 2026 23:25:19 UTC (892 KB)
[v2]
Fri, 2 Oct 2026 12:57:39 UTC (1,131 KB)
来源：arXiv：cs.LG · arxiv.org