The Constant Geometric Speed Schedule for Adiabatic State Preparation

The efficiency of adiabatic quantum evolution is governed by the evolution time $T$, which typically scales as $\mathcal{O}(Δ^{-2})$ with the minimum energy gap $Δ$. However, the rigorous lower bound is $\mathcal{O}(LΔ^{-1})$, where $L$ is the adiabatic path length. Although $L$ is formally upper-bo