  Hanoi network has a one-dimensional periodic lattice as its main structure
with additional long-range edges, which allow having efficient quantum walk
algorithm that can find a target state on the network faster than the
exhaustive classical search. In this article, we use regular quantum walks and
lackadaisical quantum walks respectively to search for a target state. From the
curve fitting of the numerical results for Hanoi network of degree three and
four we find that their running time for the regular quantum walks followed by
amplitude amplification scales as $\mathcal{O}\left(N^{0.79} \sqrt{\log
N}\right)$ and $\mathcal{O}\left(N^{0.65} \sqrt{\log N}\right)$ respectively.
And for the search by lackadaisical quantum walks the running time scales as
$\mathcal{O}\left(N^{0.57}\log N\right)$ and $\mathcal{O}\left(N^{0.50}\log
N\right)$ respectively.
