Paper

Local and Multi-Scale Strategies to Mitigate Exponential Concentration in Quantum Kernels

Saikia, Debashis, Singh, Utkarsh, Zendejas-Morales, Claudia

2026

Overview

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\\in\\{4,6,\\dots,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.

• Publisher: Cornell University Library, arXiv.org
• Subject: Datasets / Feature maps / Similarity / Subsystems