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.
In geometrical terms, the natural parametrization of a curve is by its arc length [ 21], defined as l(s) = ∫ s 0 ∥∂s′ |Φ(s′)⟩ ∥ds′
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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.