Close the quantum query-complexity gap for Boolean Matrix Product Verification

Determine the exact quantum query complexity of Boolean Matrix Product Verification by closing the gap between the (n^{5/4}) lower bound and the \widetilde O(n^{17/12}) upper bound.

Background

The paper establishes an \Omega(n^{5/4}) quantum query lower bound and a \widetilde O(n^{17/12}) upper bound for Boolean Matrix Product Verification on n times n Boolean matrices. Its reductions show that Boolean Matrix Product Verification, Orthogonal Vectors on n vectors of dimension n, and deciding whether a graph has diameter at most two have equivalent quantum query complexity up to constant-factor changes in instance size. Consequently, resolving the gap for any one of these problems would improve the bounds for all three. The authors further note that a lower bound of \Omega(n^{5/4+\varepsilon}) for any constant \varepsilon>0 would establish a polynomial separation from triangle finding.