The constant geometric speed (CGS) schedule achieves optimal Δ^{-1} scaling for adiabatic evolution time when path length L is gap-independent, using a segmented protocol that requires only a global gap lower bound, as shown in numerical tests on search and molecular systems.
Kato, On the adiabatic theorem of quantum mechanics, Jour- nal of the Physical Society of Japan 5, 435 (1950)
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The Constant Geometric Speed Schedule for Adiabatic State Preparation
The constant geometric speed (CGS) schedule achieves optimal Δ^{-1} scaling for adiabatic evolution time when path length L is gap-independent, using a segmented protocol that requires only a global gap lower bound, as shown in numerical tests on search and molecular systems.