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Exact simulation becomes exponentially expensive because the quantum state grows highly entangled.","posed_since":"","precise":"For a nonintegrable local spin chain (e.g. the mixed-field Ising chain $H=\\sum_i J Z_i Z_{i+1}+h_x X_i+h_z Z_i$) at infinite temperature, compute the energy diffusion constant $D$ from the Kubo formula to relative accuracy $\\epsilon$ at classical cost polynomial in $1/\\epsilon$, with an a posteriori error estimate. Operator-truncation methods such as dissipation-assisted operator evolution (Rakovszky, von Keyserlingk, Pollmann, arXiv:2004.05177) converge empirically but carry no general error guarantee. Answer: an algorithm with controlled error, or evidence that controlled accuracy needs cost exponential in $1/\\epsilon$.","problem_ref":null,"references":"","settled_by":"An algorithm with certified error bars reproducing D to 1 percent in a benchmark chain, cross-checked by an independent method on the same model.","status_note":"Truncation methods since 2020 give mutually consistent D estimates in benchmark chains without a general error guarantee.","title":"Controlled efficient computation of high-temperature diffusion 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