Author

Adam Wesolowski

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Preprint Oct 2026

Optimal query complexity for fractional quantum evolution

Given oracle access to an unknown unitary $U=e^{iH}$ , the fractional query problem asks how many queries are required to implement a noninteger power $U^t=e^{itH}$, $0<t<1$, when the spectrum is separated from the branch cut by a gap $\delta$. Quantum singular value transformation gives an upper bound of $O\!\left(\fr...

A. Liu, Adam Wesolowski, Jayne Thompson et al. · 0 citations

Preprint Sep 2026

Torsion detection in clique complexes is conditionally $QMA_1$-hard

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 combinatorial Laplacian. Deciding whether a Betti number of a clique complex is nonzero is $QMA_1$-hard, and remains so under a spectral gap promis...

Adam Wesolowski · 0 citations

Preprint Sep 2026

Average-case hardness of Betti number estimation

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 implies a series of hardness results for many problems in both classical and quantum Topological Data Analysis (qTDA). Under the classical plan...

S. Strelchuk, Sathyawageeswar Subramanian, Adam Wesolowski · 1 citation · ⚡1