When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning
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. 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.
Related
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BibTeX
@misc{peng2026when,
title = {{When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning}},
author = {Hanqiu Peng and Jianlong Lu and Ying Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.24631},
eprint = {2608.24631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24631},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning
AU - Hanqiu Peng
AU - Jianlong Lu
AU - Ying Chen
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2608.24631
UR - https://arxiv.org/abs/2608.24631
AB - 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.
ER -