We study the quantum query complexity of several basic graph problems. 1) We prove a tight $\Theta(n^{3/2})$ bound for finding a maximum-out-degree vertex in an $n$-vertex tournament, resolving a conjecture of Mande, Paraashar, and Saurabh [FSTTCS'23]. 2) Using the same proof idea, we give a direct proof that finding a...
Amin Shiraz Gilani, Nikhil S. Mande, Subhasree Patro et al.· 0 citations
Subgraph detection asks whether an $n$-vertex graph, accessed through queries to its adjacency matrix, contains a copy of a fixed graph $H$. We prove the first unconditional superlinear lower bounds on the bounded-error quantum query complexity of this problem, answering a longstanding open question. A copy of $H$ is a...
We prove the first non-trivial upper bound for the quantum query complexity of Boolean Matrix Product Verification ($\mathsf{BMPV}$), answering a longstanding open question in quantum query complexity. For $n\times n$ matrices, our upper bound is $\widetilde O(n^{17/12})$, improving on the standard $O(n^{3/2})$ bound o...
Amin Shiraz Gilani, François Le Gall, Xing-Yu Zhou· 0 citations
Smoothed analysis is a central framework in classical algorithms for explaining the performance of algorithms beyond the worst case, often explaining why algorithms perform well in practice. We initiate a systematic study of its quantum counterpart and show the following results. $(1)$ We show that there is a total fun...
