arXiv:2608.24631quant-phcs.LG2026-08

用量子纠缠特征映射捕捉变量高阶交互,提升异常检测准确率

When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning

论文配图:When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning
图 1 · 摘自论文原文
  • 设计基于纠缠泡利串的量子核,显式编码稀疏高阶块交互
  • 在三至八阶交互的合成数据上超越多种经典核方法,真实欺诈数据上表现最优
  • 适用于需要敏感识别复杂交互关系的场景,如金融风控

在许多决策系统中,相似性不仅由距离决定,更受变量间交互影响。在欺诈与异常检测中,微小局部扰动可能跨越交互敏感的决策边界,而环境距离几乎不变。为此,我们提出一种薄板交互模型和基于纠缠泡利串特征映射的交互驱动量子核。该特征映射显式编码稀疏高阶块交互。我们证明所提出的保真度核是半正定的,可精确分解为块结构形式,并对交互模式变化具有敏感性。在涵盖三、四、六、八阶交互的平衡与非平衡合成实验中,该核始终优于线性、径向基函数、拉普拉斯、多项式核及提供预设块乘积的工程化线性基线。在真实欺诈检测基准上,其在信用卡欺诈检测中达到最高均值准确率与F1,在IEEE-CIS欺诈检测中位列第二。结果表明,量子核性能取决于特征映射几何与预测结构的匹配程度,而非希尔伯特空间维度本身。由于该块分解核可在经典计算机上精确计算,研究确立了其预测与表征价值,而非计算上的量子加速。

原文摘要 · Abstract (English)

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. 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.

量子核交互建模欺诈检测

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