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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/2601.00745 |
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| _version_ | 1866911350755688448 |
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| author | Gonçalves, Demerson N. Fernandes, Tharso D. Lugao, Pedro H. G. Dias, João T. |
| author_facet | Gonçalves, Demerson N. Fernandes, Tharso D. Lugao, Pedro H. G. Dias, João T. |
| contents | We present a training-free, certified error bound for quantum regression derived directly from Pauli expectation values. Generalizing the heuristic of minimum accuracy from classification to regression, we evaluate axis-aligned predictors within the Pauli feature space. We formally prove that the optimal axis-aligned predictor constitutes a rigorous upper bound on the minimum training Mean Squared Error (MSE) attainable by any linear or kernel-based regressor defined on the same quantum feature map. Since computing this exact bound requires an intractable scan of the full Pauli basis, we introduce a Monte Carlo framework to efficiently estimate it using a tractable subset of measurement axes. We further provide non-asymptotic statistical guarantees to certify performance within a practical measurement budget. This method enables rapid comparison of quantum feature maps and early diagnosis of expressivity, allowing for the informed selection of architectures before deploying higher-complexity models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00745 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Training-Free Certified Bounds for Quantum Regression: A Scalable Framework Gonçalves, Demerson N. Fernandes, Tharso D. Lugao, Pedro H. G. Dias, João T. Quantum Physics We present a training-free, certified error bound for quantum regression derived directly from Pauli expectation values. Generalizing the heuristic of minimum accuracy from classification to regression, we evaluate axis-aligned predictors within the Pauli feature space. We formally prove that the optimal axis-aligned predictor constitutes a rigorous upper bound on the minimum training Mean Squared Error (MSE) attainable by any linear or kernel-based regressor defined on the same quantum feature map. Since computing this exact bound requires an intractable scan of the full Pauli basis, we introduce a Monte Carlo framework to efficiently estimate it using a tractable subset of measurement axes. We further provide non-asymptotic statistical guarantees to certify performance within a practical measurement budget. This method enables rapid comparison of quantum feature maps and early diagnosis of expressivity, allowing for the informed selection of architectures before deploying higher-complexity models. |
| title | Training-Free Certified Bounds for Quantum Regression: A Scalable Framework |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.00745 |