Training-Free Certified Bounds for Quantum Regression: A Scalable Framework

• URL: http://arxiv.org/abs/2601.00745v1
• Date: Fri, 02 Jan 2026 17:05:48 GMT
• Title: Training-Free Certified Bounds for Quantum Regression: A Scalable Framework
• Authors: Demerson N. Gonçalves, Tharso D. Fernandes, Pedro H. G. Lugao, João T. Dias,
• Abstract summary: We present a training-free, certified error bound for quantum regression derived from Pauli expectation values.<n>We provide non-asymptotic statistical guarantees to certify performance within a practical measurement budget.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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