Quantifying <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> -gate-count improvements for ground-state-energy estimation with near-optimal state preparation

We study the question of when investing additional quantum resources in preparing a ground state will improve aggregate runtime associated with estimating its energy. analyze Lin and Tong's near-optimal preparation algorithm show that it can reduce proxy for runtime, $T$-gate count, energy estimation near quadratically. Resource estimates are provided specify conditions under which added cost is worthwhile.