当相似性由交互驱动时：适用于状态敏感学习的量子核
When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning
- Centre for Quantitative Finance（定量金融中心）
- Risk Management Institute, National University of Singapore（新加坡国立大学风险管理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对相似性由变量交互主导的决策场景，提出基于纠缠泡利串特征映射的交互驱动量子核，经合成与真实欺诈检测基准验证，其预测性能优于多种经典核，且可在经典计算机上精确评估。
AI中文摘要：
在许多决策系统中，相似性并非仅由距离决定，而是由变量间的交互作用主导。在欺诈与异常检测场景中，微小的局部扰动可跨越对交互作用敏感的决策边界，而周围距离几乎保持不变。受此场景启发，我们提出一种薄板交互模型，以及基于纠缠泡利串特征映射构建的交互驱动量子核。该特征映射明确编码稀疏高阶块交互作用。我们证明，所得保真核为半正定核，具有精确的块分解形式，且诱导出对交互状态变化敏感的几何结构。在涵盖三阶、四阶、六阶及八阶交互作用的平衡与不平衡合成实验中，所提核始终优于线性核、径向基函数核、拉普拉斯核、多项式核，以及配备植入块乘积的工程交互线性基线。在真实欺诈检测基准上，其在信用卡欺诈检测数据集上实现最高平均准确率与F1值，在IEEE-CIS欺诈检测数据集上排名第二。这些发现表明，量子核的性能取决于特征映射几何结构与潜在预测结构的契合度，而非仅取决于希尔伯特空间维度。由于所提出的块分解核也可在经典计算机上精确评估，因此该成果确立了其预测与表征价值，而非计算层面的量子加速。
英文摘要：
Similarity in many decision systems is governed not by distance alone but by interactions among variables. In fraud and anomaly detection, small local perturbations can cross interaction-sensitive decision boundaries while leaving ambient distance almost unchanged. Motivated by this setting, we introduce a thin-slab interaction model and an interaction-driven quantum kernel constructed from entangled Pauli-string feature maps. The feature map explicitly encodes sparse high-order block interactions. We show that the resulting fidelity kernel is positive semidefinite, admits an exact block-factorized formulation, and induces a geometry sensitive to changes in interaction regime. Across balanced and imbalanced synthetic experiments spanning third-, fourth-, sixth-, and eighth-order interactions, the proposed kernel consistently outperforms linear, radial basis function, Laplacian, and polynomial kernels, as well as an engineered-interaction linear baseline supplied with the planted block products. On real fraud-detection benchmarks, it achieves the highest mean accuracy and F1 on Credit Card Fraud Detection and ranks second on IEEE-CIS Fraud Detection. Executed on a 156-qubit IBM Quantum processor in a fourth-order setting, the hardware-estimated kernel matches the noise-free simulator within seed-to-seed variability and retains its advantage over the baselines. These findings show that quantum-kernel performance depends on alignment between feature-map geometry and the underlying predictive structure, rather than on Hilbert-space dimension alone. Because the prescribed block-factorized kernel can also be evaluated exactly on a classical computer, the results establish predictive and representational value rather than computational quantum speedup.
