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.
Laplacian eigen- maps for dimensionality reduction and data representa- tion
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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.