Quantifying T-gate-count improvements for ground-state-energy estimation with near-optimal state preparation

Quantum computers will enable high-accuracy quantum simulations of physical systems, provided that states with reasonable overlap with the ground state can be efficiently prepared. In this Letter, the authors articulate conditions in which quadratic runtime speedups are plausible for ground-state energy estimation by translating a near-optimal ground-state preparation scheme into explicit circuits and estimating the cost in a model relevant to their fault-tolerant implementation.