量子支持向量机在表格数据上表现不如经典方法，但为未来研究提供明确方向。
Benchmarking Quantum Kernel Support Vector Machines Against Classical Baselines on Tabular Data: A Rigorous Empirical Study with Hardware Validation
- 在9个数据集上对比量子与经典核方法，严格验证结果可靠性。
- 量子模型学习曲线更陡，但始终无法超越最优经典模型性能。
- 仅量子核训练在乳腺癌数据上略胜，但耗时超经典方法2000倍。
量子核方法被视为利用近期量子计算机进行监督学习的有前景路径，但与强古典基线的严谨基准测试仍稀缺。本文对量子核支持向量机（QSVM）在九个二分类数据集、四种量子特征映射、三种经典核函数及多重噪声模型下进行了全面实证研究，共执行970次实验，采用严格嵌套交叉验证。分析涵盖四个阶段：(i) 统计显著性检验显示29组量子-经典对比中无一在α=0.05水平显著；(ii) 六个训练比例的学习曲线分析表明，六组数据上量子模型斜率更陡，但仍未能缩小与最佳经典基线的差距；(iii) 在IBM ibm_fez (Heron r2)硬件上验证，六个实验的核保真度均≥0.976；(iv) 种子敏感性分析确认可复现性（平均CV 1.4%）。Kruskal-Wallis因子分析表明，数据集选择主导性能方差（ε²=0.73），核类型仅解释9%。谱分析揭示：当前量子特征映射产生的特征值谱要么太平，要么太集中，缺乏最优经典核（RBF）的中间分布特征。通过核目标对齐进行量子核训练（QKT）获得唯一有竞争力结果——乳腺癌数据平衡准确率0.968，但计算开销达经典方法约2000倍。研究提供量子核方法的实用指导，完整基准套件已公开，便于复现与扩展。
原文摘要 · Abstract (English)
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation. Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at $α= 0.05$; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity $r \geq 0.976$ across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%). A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance ($\varepsilon^2 = 0.73$), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead. Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.
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