Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods

Gonçalves, Demerson N.; Fernandes, Tharso D.; Cordeiro, Andrias M. M.; Lugao, Pedro H. G.; Dias, João T.; Araújo Moreira, Fernando M.

doi:10.3390/quantum8030073

Open AccessArticle

Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods

by

Demerson N. Gonçalves

^1,2

,

Tharso D. Fernandes

^2,3,*

,

Andrias M. M. Cordeiro

⁴,

Pedro H. G. Lugao

⁴,

João T. Dias

^2,5

and

Fernando M. Araújo Moreira

²

¹

Department of Mathematics, Federal Center for Technological Education Celso Suckow da Fonseca (CEFET-RJ), Petrópolis 25609-010, RJ, Brazil

²

Instituto Militar de Engenharia (IME), Rio de Janeiro 22290-270, RJ, Brazil

³

Department of Pure and Applied Mathematics, Federal University of Espírito Santo (UFES), Alegre 29500-000, ES, Brazil

⁴

Department of Computer Engineering, CEFET-RJ, Petrópolis 25609-010, RJ, Brazil

⁵

Department of Telecommunications Engineering, CEFET-RJ, Rio de Janeiro 20271-110, RJ, Brazil

^*

Author to whom correspondence should be addressed.

Quantum Rep. 2026, 8(3), 73; https://doi.org/10.3390/quantum8030073

Submission received: 12 June 2026 / Revised: 19 July 2026 / Accepted: 20 July 2026 / Published: 31 July 2026

(This article belongs to the Topic Quantum Computing: Latest Advances and Prospects)

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Abstract

The minimum accuracy heuristic provides a training-free way to evaluate quantum feature maps, but its original formulation assumes balanced datasets, requires an exhaustive Pauli-axis scan, and lacks a formal lower-bound interpretation. In this work, we generalize the metric to arbitrary binary datasets and prove that the resulting generalized minimum accuracy, denoted

R_{min}

, is a certified lower bound on the optimal empirical accuracy

R^{*}

achievable by linear classifiers in the same feature space. To improve scalability, we introduce Monte Carlo axis-selection strategies that estimate

R_{min}

from random subsets of Pauli-feature axes and derive quantile-coverage guarantees for sampling high-accuracy directions. We validate the framework using exact statevector simulations of an

n = 6

qubit quantum feature map, corresponding to

d = 4^{6} = 4096

Pauli axes, over 30 independent runs on five synthetic datasets. The proposed methods sample as few as 60 axes, produce lower-bound estimates and achieve speedups of approximately

27 \times

to

68 \times

compared with exhaustive evaluation. The results support generalized minimum accuracy as a scalable and theoretically grounded tool for pre-screening quantum feature maps in simulated quantum-kernel workflows.

Keywords: quantum machine learning; quantum kernel methods; minimum accuracy; feature map evaluation; Pauli observables

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MDPI and ACS Style

Gonçalves, D.N.; Fernandes, T.D.; Cordeiro, A.M.M.; Lugao, P.H.G.; Dias, J.T.; Araújo Moreira, F.M. Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods. Quantum Rep. 2026, 8, 73. https://doi.org/10.3390/quantum8030073

AMA Style

Gonçalves DN, Fernandes TD, Cordeiro AMM, Lugao PHG, Dias JT, Araújo Moreira FM. Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods. Quantum Reports. 2026; 8(3):73. https://doi.org/10.3390/quantum8030073

Chicago/Turabian Style

Gonçalves, Demerson N., Tharso D. Fernandes, Andrias M. M. Cordeiro, Pedro H. G. Lugao, João T. Dias, and Fernando M. Araújo Moreira. 2026. "Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods" Quantum Reports 8, no. 3: 73. https://doi.org/10.3390/quantum8030073

APA Style

Gonçalves, D. N., Fernandes, T. D., Cordeiro, A. M. M., Lugao, P. H. G., Dias, J. T., & Araújo Moreira, F. M. (2026). Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods. Quantum Reports, 8(3), 73. https://doi.org/10.3390/quantum8030073

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Certified Lower Bounds and Efficient Estimation of Minimum Accuracy in Quantum Kernel Methods

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