Perfect state transfer, Equitable partition and Continuous-time quantum walk based search

TL;DR

This paper explores a quantum search algorithm using continuous-time quantum walks, introducing equitable partition and perfect state transfer to improve calculation of success probability and search time.

Contribution

It presents a novel approach combining equitable partition and perfect state transfer for analyzing quantum walk based search algorithms.

Findings

Successfully calculates success probability and finding time for specific graphs.

Demonstrates the effectiveness of equitable partition and perfect state transfer in quantum search.

Provides examples illustrating the calculation methods.

Abstract

In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding time of the search algorithm. In addition, we gave some examples of graphs that we can calculate the success probability and the finding time.