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 first need to use Lemma C.4 to obtain the unitary Uexi , which has complexity O (log |Ni|)
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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.