On the probability of finding marked connected components using quantum walks

TL;DR

This paper analyzes the probability of locating marked connected components in a graph using quantum walks, providing upper bounds and discussing implications for quantum search efficiency.

Contribution

It introduces new bounds on the probability of finding marked components with quantum walks and explores the limitations of quantum speed-up in such scenarios.

Findings

Two upper bounds on the probability of finding marked vertices

Quantum walk search may not outperform classical search for adjacent marked vertices

Directions for future research in quantum walk search algorithms

Abstract

Finding a marked vertex in a graph can be a complicated task when using quantum walks. Recent results show that for two or more adjacent marked vertices search by quantum walk with Grover's coin may have no speed-up over classical exhaustive search. In this paper, we analyze the probability of finding a marked vertex for a set of connected components of marked vertices. We prove two upper bounds on the probability of finding a marked vertex and sketch further research directions.