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

TL;DR

This paper analyzes how investing quantum resources in state preparation can significantly reduce the $T$-gate count, a key metric, for ground-state energy estimation, providing conditions for when such investment is beneficial.

Contribution

It evaluates Lin and Tong's near-optimal state preparation algorithm, demonstrating near-quadratic reduction in $T$-gate count for energy estimation and outlining when additional resources are justified.

Findings

Near-quadratic reduction in $T$-gate count achieved

Resource estimates specify when investment improves efficiency

Conditions identified for cost-effective state preparation

Abstract

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