# Comment on Nahimovs et al. `On the probability of finding marked connected components using quantum walks'

## TL;DR

This comment paper identifies and corrects misconceptions in Nahimovs et al.'s work on quantum walks, specifically regarding stationary states and probability bounds, clarifying the conditions under which their theorems hold.

## Contribution

It highlights incomplete conditions in Theorem 2 and corrects the derivation of the coefficient in Theorem 3, refining the original results.

## Key findings

- Theorem 2 is only valid when unmarked vertices form a single connected component.
- The derivation of the coefficient in Theorem 3 was corrected.
- Upper bounds for the coefficient were established.

## Abstract

In this comment paper we present two misconceptions found in paper of Nahimovs et al. \emph{On the probability of finding marked connected components using quantum walks}. First, we show that the Theorem 2 (sufficient and necessary condition for a state to be stationary) is incomplete -- it works only if unmarked vertices form a single connected component. Second, we correct derivation of \emph{a} coefficient in the Theorem 3 (lower bound on the probability) and show how to upper bound value of \emph{a}.