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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.
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Comment on 'Supervised quantum machine learning models are kernel methods'

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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

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