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Whether there is a real exponential gap for a growing family of real molecules is disputed.","posed_since":"2022","precise":"Fix a size-indexed chemical family, for example iron-sulfur clusters with $N_{\\mathrm{Fe}} = 2, 4, 8, ...$ iron centers and active spaces of N orbitals growing linearly with $N_{\\mathrm{Fe}}$, or linear transition-metal chains of length N. For ground-state energy to chemical accuracy ($1.6\\,\\mathrm{mHa}$), compare the scaling with N of the best classical cost (DMRG, coupled cluster, selected CI, quantum Monte Carlo) with that of quantum phase estimation including the cost of preparing a state with sufficient ground-state overlap; decide whether the ratio grows exponentially in N. Lee et al. (arXiv:2208.02199, Nature Communications 2023) found no evidence of a generic exponential advantage.","problem_ref":null,"references":"","settled_by":"For a stated family, a proof or convincing size-series demonstration of exponential classical cost and polynomial quantum cost including state preparation, or classical algorithms with polynomial scaling on it.","status_note":"","title":"Is there exponential quantum advantage for molecular ground-state 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