2026/02/28 by Claudia Zendejas-Morales, Debashis Saikia, Utkarsh Singh
Physics and Astronomy · #quant-ph
18 pages, 10 figures. Revised theoretical presentation and proofs; clarified notation, experimental protocol, and figure captions; updated references. Experimental results and main conclusions unchanged
arxiv created 2026/08/03 · arxiv updated 2026/08/05
Fidelity-based quantum kernels provide a direct interface between quantum feature maps and classical kernel methods, but they can exhibit exponential concentration: with increasing system size or circuit expressivity, the Gram matrix approaches the identity and suppresses informative similarity structure. We present an empirical study of two mitigation strategies implemented in Qiskit: (i) local (patch-wise) kernels that aggregate subsystem similarities, and (ii) multi-scale kernels that mix local and global similarity across patch granularities. We benchmark baseline, local, and multi-scale kernels under matched preprocessing, splits, and SVM protocols on several tabular datasets, sweeping the feature dimension d∈\4,6,…,20\. We report concentration diagnostics based on off-diagonal kernel statistics, spectral richness via effective rank, and centered alignment with labels. Across datasets, local and multi-scale constructions consistently mitigate concentration and yield richer kernel spectra relative to the global fidelity baseline, while the impact on classification accuracy depends on the dataset and dimension.