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It is conjectured that every circuit family provably free of this flatness can also be imitated by a classical computer, which would remove the point of using it.","posed_since":"2023","precise":"For parametrized circuits with loss $L(\\theta) = \\operatorname{Tr}[O U(\\theta) \\rho U(\\theta)^{\\mathrm{dag}}]$ whose gradient variance provably decays at most polynomially in qubit number $n$, is there always a classical algorithm that, after collecting $\\operatorname{poly}(n)$ measurement data from a quantum device once, estimates $L(\\theta)$ to $1/\\operatorname{poly}(n)$ for any $\\theta$ in $\\operatorname{poly}(n)$ time? Cerezo et al. (arXiv:2312.09121, Nat. Commun. 16, 7907, 2025) argue yes for known families. An answer is a proof, or a barren-plateau-free family with a hardness proof.","problem_ref":"e7cbf7c913e74e020c7051ef0f403a5f392f315c19f1658695998b1b77c354d9","references":"","settled_by":"A general simulation theorem under the polynomial-gradient-variance assumption, or a counterexample family with a complexity-theoretic hardness proof.","status_note":"","title":"Does absence of barren plateaus imply classical 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