Sharp Target-Domain Certificates for Quantum-Kernel Advantage under Distribution Shift

Abstract:Quantum predictive advantage under shift usually requires known target labels. We derive the assumption-free sharp identified interval for the finite-batch advantage of a fixed candidate over the best member of a prespecified fixed classical-kernel family under any bounded loss and unrestricted completions of the unaudited labels; zero-one accuracy has exact closed-form partial-label updates. Across eight security shifts, zero-label upper endpoints against 115 classical kernels span 0.002-0.088. Retrospective auditing reduces every endpoint to 0.010 with 0-33 of 500 labels, including entangling-ZZ models. Prospective corroboration on two eligible tasks met predefined criteria: four task-classifier medians require 0-3 labels (overall median 0; maximum 76), and all 20 realized effects are negative; a third task fails its feature gate. Protocol controls reverse an apparent advantage, while finite-shot noise can increase predictive distinctness without useful advantage. The framework separates protocol validity, target predictive indispensability, and quantum relevance.

42 pages, 7 figures; 16-page Supplementary Information available as ancillary material. Submitted to EPJ Quantum Technology

arXiv:2610.00080 [quant-ph]

(or arXiv:2610.00080v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.00080 Focus to learn more arXiv-issued DOI via DataCite

supplementary.pdf

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