测试量子核在真实硬件上保留数据几何结构的能力，发现门抖动最保真。
Statevector-Referenced Geometry Survival of a Four-Qubit ZZ Quantum Kernel on IBM Quantum Hardware: A Fixed-Subset Diagnostic Across Three Execution Configurations
- 用固定四比特ZZ映射核在真实量子硬件上测试数据几何保真度。
- 三种配置下均保持正半定核矩阵，中心态矢量对齐率达0.933-0.989。
- 门抖动最接近理想态，但与标签对齐反而最低，反映保真与任务相关性分离。
量子核方法将数据集的几何结构编码在格拉姆矩阵中，因此硬件核上的学习结果依赖于目标几何结构能否在执行中保持。本文针对一个固定的四比特ZZ特征映射核，在N=24个真实室内空气质量窗口数据上，于ibm_fez（每电路1024次测量）上测试了基线、仅动态解耦、仅门抖动三种配置下的几何生存能力，每种为单个非交错作业。所有配置均返回完整、有限、半正定的格拉姆矩阵，中心态矢量几何结构保留程度较高但不完全（全矩阵中心核对齐，CKA：0.933–0.989）。门抖动在所有几何轴上最为保真，唯一显著优于基线的改进体现在自助法验证的斯皮尔曼相关性、平均绝对误差和全矩阵CKA诊断；仅动态解耦与基线无显著差异。残余硬件畸变而非有限采样是主要偏差来源。然而，保真度与标签对齐呈反向关系：最保真的配置具有最低的中心核-目标对齐，甚至低于状态矢量与硬件的标签置换参考值。我们认为硬件微小提升是由于非仿射畸变的归一化效应，而非实际信号。这些为单一后端、单次作业的描述性结果，非因果性缓解效果评估；不主张量子优势、硬件分类器优越性或预测能力。实现保真度与任务相关性应独立报告，硬件量子机器学习研究需同时披露两者。
原文摘要 · Abstract (English)
Quantum-kernel methods encode a dataset's geometry in a Gram matrix, so learning claims on hardware kernels assume the intended geometry survives execution. We measure that survival for one frozen four-qubit ZZ feature-map kernel on $N=24$ real indoor air-quality windows, reconstructed on ibm_fez (1024 shots per circuit) under baseline, dynamical decoupling alone, and gate twirling alone, each a single non-interleaved job. Every configuration returned a complete, finite, positive-semidefinite Gram matrix and preserved the centered statevector geometry to a substantial but incomplete descriptive degree (full-matrix centered kernel alignment, CKA, 0.933-0.989). Gate twirling was most faithful on every reported geometry axis, with the only jackknife-resolved improvement over baseline (persisted Spearman, mean absolute error, and full-matrix CKA diagnostics); dynamical decoupling alone was not separated from baseline at the frozen-window scale. Residual hardware distortion, not finite sampling, dominates the discrepancy. Yet fidelity and label alignment were reversed: the most faithful configuration had the lowest centered kernel-target alignment, which sits at or below label-permutation references for statevector and hardware alike. We read the small hardware uplift as a normalization property of the non-affine distortion, not captured signal. These are descriptive results for single jobs on one backend, not causal mitigation-efficacy estimates; no quantum-advantage, hardware-classifier-superiority, or forecasting claim is made. Implementation fidelity and task relevance are distinct axes; hardware quantum machine-learning studies should report both.
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