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Optimal query complexity for fractional quantum evolution
Anthony Yuezhang Liu, Adam Wesołowski, Jayne Thompson +2
Given oracle access to an unknown unitary , the fractional query problem asks how many queries are required to implement a noninteger power , , when…
Quantum Log-Determinant Methods for Torsion-Sensitive Topological Data Analysis
Dimitrios Thanos, Caesnan Leditto, Adam Wesolowski +2
Betti numbers are central to topological data analysis but fail to capture torsion in integral homology. Torsion can distinguish topological structures with identical Betti numbers…
Torsion detection in clique complexes is conditionally -hard
Adam Wesołowski
Quantum algorithms for topological data analysis compute Betti numbers, the ranks of the homology groups of a simplicial complex, which can be read off from the kernel of a combina…
Average-case hardness of Betti number estimation
Sergii Strelchuk, Sathyawageeswar Subramanian, Adam Wesołowski
We establish the average-case hardness of Betti number estimation on random clique complexes via a reduction from the planted clique problem. We further show that our reduction imp…