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.
2), the energy gap ∆( s) often becomes small only in a very narrow region of s, so a uniform grid may fail to capture the point where long evolution time is required
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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.