  Carlotto, Chodosh and Rubinstein have studied the convergence rate of the
Yamabe flow. Inspired by their result, we study the convergence rate of the
$Q$-curvature flow in this paper. In particular, we provide an example of a
slowly converging $Q_6$-curvature flow in dimension 6, in constrast to the
dimension 2 case, where the $Q$-curvature flow always converges exponentially.
