AI 中文总结
该研究提出用关联分形维数D₂作为量子核的先验量子比特预算，通过FD-ASE选择编码坐标，在多数据集和IBM Quantum上验证其可避免角度编码量子核崩溃，确定核活性上限。
AI 中文摘要
表格数据上的角度编码量子核会在特征映射宽度超过数据本征维数时发生崩溃。我们提出将关联分形维数D₂作为先验量子比特预算：采用FD-ASE算法选择的D₂个坐标进行编码，而非使用PCA-95%宽度或全部E个属性。在9个数据集和状态矢量模拟器（n=32）上，q=D₂时的单层ZZ保真度核保持几何活性，而在PCA-95%宽度下的同一核已崩溃。该预算依赖于映射：乘积态和IQP映射会超出该预算；添加第二层ZZ层则会低于该预算。密集角度打包和重上传编码在分形q处仍保持活性，但当将PCA-95%特征堆叠到这些量子比特上时则不再如此。缩小角度带宽会使ZZ核的拐点后移；拉伸带宽则会更早使核崩溃。在IBM Quantum（ibm_fez，256次采样，n=8）上，分形宽度处的单层ZZ核与精确核匹配（MAE=0.021）；超过该宽度后，硬件和模拟器的核均已崩溃。该上限是给定带宽下映射-数据对的属性，而非仅经典表格的属性。
英文摘要
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.
Comments28 pages, 12 figures. Submitted to Quantum Machine Intelligence
