Removal of the logarithmic factor in query complexity

Determine whether the remaining logarithmic factor in the query-complexity upper bound for estimating the state frame potential can be removed.

Background

The paper establishes a query complexity of approximately $\widetilde{O}(\sqrt{t}/\varepsilon)$ for estimating the order-$t$ state frame potential, with the upper and lower bounds matching up to logarithmic factors. The authors explicitly identify removal of this residual logarithmic factor as a natural unresolved question.