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Sign inePrint 2024/555 claimed a polynomial-time quantum algorithm for LWE at certain polynomial modulus-to-noise ratios, using complex Gaussians and a windowed QFT, which would have given quantum algorithms for GapSVP and SIVP at approximation factors . It would not have broken the standardised ML-KEM/ML-DSA parameters directly but would have undermined their worst-case foundations.
On 18 April 2024 the author reported that Step 9 of the algorithm contains a bug he does not know how to fix, found by Hongxun Wu and independently Thomas Vidick, and that the polynomial-time claim does not hold. The paper remains online with this note.
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Hongxun Wu and Thomas Vidick independently found a bug in Step 9 (Section 3.5.9); the author confirmed it cannot be fixed as written.
The author leaves the complex-Gaussian and windowed-QFT parts in place. It is open whether they yield a nontrivial quantum algorithm for any LWE variant, for example with super-polynomial modulus or extra samples.
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