aiqbench analysis
This paper provides a rigorous correction to the mathematical proofs in Schuld's foundational work on supervised quantum machine learning, clarifying how errors in deriving Fourier coefficients coincidentally canceled out in previous examples. By fixing these derivations, researchers can now accurately compute quantum kernels without relying on accidental cancellations, strengthening the theoretical underpinnings of this specific subfield.
Comment on 'Supervised quantum machine learning models are kernel methods'
arXiv:2608.24923v1 Announce Type: new Abstract: We identify a few small errors in the proof of Theorem 1 in M. Schuld, 'Supervised quantum machine learning models are kernel methods' (arXiv:2101.11020v2), Appendix A. These do not affect the validity of the theorem, but do matter if one wants to use the appendix to explicitly compute the Fourier coefficients of a quantum kernel. We give the corrected derivation, and additionally show that the paper's worked cosine-kernel example contains a second, unrelated error that happens to cancel the first, thereby coincidentally yielding the correct result.
Abstract:We identify a few small errors in the proof of Theorem 1 in M. Schuld, 'Supervised quantum machine learning models are kernel methods' (arXiv:2101.11020v2), Appendix A. These do not affect the validity of the theorem, but do matter if one wants to use the appendix to explicitly compute the Fourier coefficients of a quantum kernel. We give the corrected derivation, and additionally show that the paper's worked cosine-kernel example contains a second, unrelated error that happens to cancel the first, thereby coincidentally yielding the correct result.
Comment on arXiv:2101.11020v2
arXiv:2608.24923 [quant-ph]
(or arXiv:2608.24923v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.24923 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 178 words
Related coverage
Synthesis Superintelligence: from Semiconductors to Superconductors — Periodic Labs’ Liam Fedus and Ekin Dogus Cubuk
Latent Space · Oct 8, 2026

Quantum Machine-Learning Design Targets Training And Scaling Barriers
The Quantum Insider · Jul 28, 2026

Quantum Phases Classified From Subsystems of Four Sites or Less
Quantum Zeitgeist · Jul 21, 2026
Towards Surrogate Based Dequantization of Quantum Reinforcement Learning
arXiv · Sep 16, 2026