The Sandwich test estimates <ψ|U^k|ψ> with total run time O(k^2 ln k / ε^2 s_min^6), skipping small-amplitude steps via a random binary sum tree, but the key assumption that s_min stays large is unproven.
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Sandwich test for Quantum Phase Estimation
The Sandwich test estimates <ψ|U^k|ψ> with total run time O(k^2 ln k / ε^2 s_min^6), skipping small-amplitude steps via a random binary sum tree, but the key assumption that s_min stays large is unproven.