# Upperbounds on the probability of finding marked connected components using quantum walks

## TL;DR

This paper investigates the limitations of quantum walk search algorithms in finding multiple marked vertices, establishing upper bounds on success probabilities and demonstrating potential slowdowns even on real-world networks.

## Contribution

It provides new theoretical upper bounds on the probability of locating marked vertices using quantum walks, especially in complex graph structures.

## Key findings

- Quantum walks can be significantly less effective in finding multiple marked vertices.
- Upper bounds demonstrate potential slowdowns in quantum search on real-world networks.
- Quantum search may be inefficient even when multiple marked vertices are present.

## Abstract

Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked vertices, that if only one of them is marked. In this paper, we analyze the probability of finding any of marked vertices in such scenarios and prove upper bounds for various sets of marked vertices. We apply the upper bounds to large collection of graphs and show that the quantum search may be slow even when taking real-world networks.