量子核在高阶异或分类中表现更优，尤其当特征数量多时。
Quantum Kernels for Parity-Structured Classification: A Hybrid Pipeline
- 用二值编码与量子特征映射结合，显化异或结构。
- 11个特征时，量子核准确率达66.3%，远超经典方法的54.3%。
- 量子优势在复杂度高时显现，适合研究量子机器学习边界。
异或（XOR）分类需要捕捉离散的高阶特征交互，而传统核函数难以高效处理。本文研究量子核优势与异或复杂度的关系，即参与异或规则的特征数量。采用ZZ量子特征映射与二值{0, π}编码（特征经中位数阈值化后输入电路），以揭示异或结构。通过对比相同二值特征上训练的RBF SVM，分离编码与电路效应：低复杂度（n=5）下，二值RBF达83.4%±1.7%，量子核为81.2%±1.9%，表明编码主导性能；高复杂度（n=11，11量子比特，r=3次重复）下，所有经典方法接近随机（约50%），二值RBF仅达54.3%±1.1%，量子ZZ核达66.3%±3.2%（10种子平均±标准差），比经典方法高出12.0个百分点，核-目标对齐度达0.094±0.020，约为经典的7倍（0.013±0.001）。结果表明，异或复杂度是体现真正量子核优势的关键维度。
原文摘要 · Abstract (English)
Parity (XOR) classification requires detecting discrete, high-order feature interactions that smooth classical kernels cannot efficiently capture. We study how quantum kernel advantage depends on parity complexity, the number of features entering the XOR rule, and find a clear threshold behavior. We pair a ZZ quantum feature map with binary {0, pi} encoding (features median thresholded before circuit input) to expose parity structure. A binary encoding ablation, RBF SVM trained on the identical {0, pi} features, separates encoding from circuit effects: at low complexity (n = 5 features), binary RBF achieves 83.4% +/- 1.7% and the quantum kernel 81.2% +/- 1.9%, showing encoding drives performance there. At high complexity (n = 11 features, 11 qubits, r = 3 ZZ repetitions), all classical methods collapse to near-random (approx. 50%), binary RBF reaches only 54.3% +/- 1.1%, and the quantum ZZ kernel achieves 66.3% +/- 3.2% (mean +/- std, 10 seeds), a +12.0 percentage-point margin over the binary ablation and approx. 7x higher kernel-target alignment (0.094 +/- 0.020 vs. 0.013 +/- 0.001). These results identify parity complexity as a concrete axis along which genuine quantum kernel advantage, not attributable to encoding alone, emerges.
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