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arXiv · 1209.2871

Spatial Search Algorithms on Hanoi Networks

Franklin L. Marquezino·Renato Portugal·Stefan Boettcher
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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.

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Franklin L. Marquezino, Renato Portugal, Stefan Boettcher. 2012-09-13. Spatial Search Algorithms on Hanoi Networks. https://doi.org/10.1103/physreva.87.012329

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