A quantum algorithm for local dimension and curvature estimation is proposed, but the claimed exponential speedup rests on unproven spectral-gap assumptions and an incorrect least-squares derivation.
It can be seen that the first column of this unitary is P j,xj ∈Ni |j⟩ xi
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Quantum Algorithm for Estimating Intrinsic Geometry
A quantum algorithm for local dimension and curvature estimation is proposed, but the claimed exponential speedup rests on unproven spectral-gap assumptions and an incorrect least-squares derivation.