Abstract
Variational quantum eigensolvers fail before optimization begins when strong correlation splits the molecular energy landscape into competing basins and the initial state selects a non-ground-state basin. We introduce a geometry-conditioned preconditioner P_eq:R↦θ₀ constrained by the SE(3) covariance of the molecular Hamiltonian, so that nuclear geometry is mapped directly into circuit parameters in the correlated ground-state basin. This basin localization changes the relevant gradient statistics from concentration controlled to curvature controlled. In statevector benchmarks on six stretched molecules, P_eq reduces Hartree--Fock initialization errors by factors of 38×--6250×, reaches sub-mHa initialization in CO, LiH, and H₈, and places N₂, H₂O, and BeH₂ in the mHa-scale correlated basin. In disordered H₁₀ chains, equivariant basin targeting and stochastic escape reach unit success probability at fixed optimization budget. The procedure performs basin selection before the shot-limited quantum loop; the quantum circuit then refines correlation inside the selected basin.