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

2026-08-25

AI Summary

本文针对决策系统中变量间交互影响相似性的问题，提出了一种基于纠缠Pauli-string特征映射的交互驱动量子核方法，并在欺诈检测等任务上展示了其优越性能。

Abstract

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.

Problem

• interaction-driven
• decision boundaries
• anomaly detection
• quantum kernels

Innovation

• thin-slab interaction model
• entangled Pauli-string feature maps
• fidelity kernel
• block-factorized formulation
• regime-sensitive learning