Quantum walk-based search and centrality

TL;DR

This paper explores how the success probability of quantum walk-based search algorithms varies with the centrality of the marked vertex in different graph structures, revealing that higher centrality does not always lead to higher success.

Contribution

It analyzes the relationship between vertex centrality and search success probability in quantum walks, highlighting non-intuitive effects across various graph structures.

Findings

Maximum search probability does not always increase with centrality.

A relationship exists between search probability frequency and vertex centrality.

Centrality's impact on search success varies depending on graph structure.

Abstract

We study the discrete-time quantum walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and the position of the marked vertex, in particular its centrality. We find that the maximum value of the search probability does not necessarily increase as the marked vertex becomes more central and we investigate an interesting relationship between the frequency of the successful search probability and the centrality of the marked vertex.