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.
In this step, we need to perform principal component analysis on∝ C † i Ci to find the local dimension di
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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.