Quantum search on Hanoi network

Hanoi network (HN) 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 paper, 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 HN of degrees three and four, we find that their running time for the regular quantum walks are followed by amplitude amplification scales as (N0.79logN) and (N0.65logN), respectively. For the search by lackadaisical quantum walks, the running time scales are as (N0.57logN) and (N0.50logN), respectively.