Answers are grounded in this paper and cite their sources.
This note examines quantum speedup claims for evaluating Riemann zeta function, indicating flaws in the approach.
Wei et al. (Nat. Commun., 2026; preprint arXiv:2511.11199v1) report a quantum algorithm for ζ(½+it) and compare its cost against direct Riemann–Siegel summation. This note examines that comparison. The speedup claim is correct against the baselines the paper names, and correct for a single isolated evaluation. It is, however, applied to locating and verifying zeros, which is a bulk task, and the classical state of the art for bulk evaluation is amortized. Odlyzko–Schönhage (1988) amortizes to T^ε per point, for every ε > 0, over blocks of length T^(1/2) after one precomputation, where the quantum method offers no amortization mechanism at all and pays its per-point cost every time; Hiary's amortized method (Math. Comp., 2011) reaches the same T^(1/4) exponent classically fifteen years earlier. Neither is cited in the preprint's 47-item reference list — a finding scoped to arXiv:2511.11199v1 and to that version only, for reasons given below. The Hiary paper the preprint does cite is the later Annals method, not the amortized one. Odlyzko–Schönhage is present in the source bibliography database but uncited, one of 16 uncited entries of 65, a set that also contains Riemann (1859); no intent is inferred. One argument is developed and one is withdrawn. The withdrawn one is a precision penalty. A measurement made for this note over 6200 Gram points spanning six decades of height finds |Z| height-flat (fitted slope −0.00005941, R² = 0.000333), so the sampling resolution δ is a large constant factor, not an asymptotic penalty. What survives is practical rather than asymptotic and rests on a single datum, the most extreme value in the sources obtained here; no distribution for that tail is stated in any of them, so the datum is not an upper bound on the precision required. The argument that carries the weight is categorical rather than complexity-theoretic: amplitude estimation returns confidence intervals, whereas rigorous verification of the Riemann Hypothesis to a given height requires certified enclosures. Platt–Trudgian's accounting of their 3×10¹² computation supports this, attributing a 725× cost of rigour to interval arithmetic and sampling rate and explicitly not to precision. Separately, the paper's correspondence theorem is shown to hold at every zero in the strip, not only on the critical line; this is a statement about the construction, which is therefore coextensive with the Riemann Hypothesis rather than evidence bearing on it. Nothing here bears on the hypothesis itself, and nothing here disputes the physics. Every claim is traced to a hashed artifact and classified by the strength of its warrant. The bibliography findings are scoped to arXiv:2511.11199v1: the published record is an Accelerated Article Preview carrying no reference list, and the published version is known to differ from v1, so a recheck is registered against the edited version when it appears. Three blockers are left open and stated rather than closed — the unavailable published reference list, the absent tail distribution, and what actually sets the operative resolution for sign-change-based verification, given that precision was demonstrably not the binding classical constraint. An appendix registers one pre-specified, falsifiable prediction about quantum block-amortized cost.
No takes yet. Share an insight, caveat, or question.
Papanokechi (2026) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: