Spatial Search Algorithms on Hanoi Networks

TL;DR

This paper analyzes quantum spatial search algorithms on Hanoi networks, demonstrating that Tulsi's method and non-Groverian coins can significantly improve search efficiency, with results supported by numerical simulations.

Contribution

It introduces the application of Tulsi's extension and non-Groverian coins to enhance quantum search algorithms on Hanoi networks, providing scaling analysis and numerical validation.

Findings

Tulsi's technique accelerates the quantum search process.

Non-Groverian coins improve efficiency without Tulsi's method.

The algorithm's total cost scales favorably with network size.

Abstract

We use the abstract search algorithm and its extension due to Tulsi to analyze a spatial quantum search algorithm that finds a marked vertex in Hanoi networks of degree 4 faster than classical algorithms. We also analyze the effect of using non-Groverian coins that take advantage of the small world structure of the Hanoi networks. We obtain the scaling of the total cost of the algorithm as a function of the number of vertices. We show that Tulsi's technique plays an important role to speed up the searching algorithm. We can improve the algorithm's efficiency by choosing a non-Groverian coin if we do not implement Tulsi's method. Our conclusion is based on numerical implementations.