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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.16097 |
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| _version_ | 1866915803813642240 |
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| author | Zendejas-Morales, Claudia Saikia, Debashis Singh, Utkarsh |
| author_facet | Zendejas-Morales, Claudia Saikia, Debashis Singh, Utkarsh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local and Multi-Scale Strategies to Mitigate Exponential Concentration in Quantum Kernels Zendejas-Morales, Claudia Saikia, Debashis Singh, Utkarsh Quantum Physics 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. |
| title | Local and Multi-Scale Strategies to Mitigate Exponential Concentration in Quantum Kernels |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.16097 |