Is there exponential quantum advantage for molecular ground-state energies?

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.

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.