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Title: Scaling of ground-state overlap for classically preparable trial states
Plain: Quantum phase estimation needs a starting state that resembles the true ground state. If the best starting states that ordinary computers can prepare become exponentially worse as molecules grow, the quantum speedup disappears.
Precise: For strongly correlated molecules and clusters (e.g. iron-sulfur clusters with $N_{\mathrm{Fe}}$ iron atoms), determine how the maximal overlap $\mid\langle \phi \mid \psi_0\rangle\mid^2$ between the ground state $\psi_0$ and states $\phi$ preparable classically in poly time (bounded-bond-dimension MPS, broken-symmetry determinants and short sums of them) scales with system size; exponential decay would remove the exponential advantage of phase estimation.
Settled by: Computed overlaps for a size series of a chemically relevant family large enough to fit the scaling, or a proof for a model family.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 2022