Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1903.01482 · Quantum Information Processing

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

Adam Glos, Nikolajs Nahimovs, Konstantin Balakirev, Kamil Ravilevich Khadiev

Published Jan 1, 2021• 11 citations
arXivHTMLPDF
DOI
10.1007/s11128-020-02939-4

Related papers

On the probability of finding marked connected components using quantum walks

Nikolajs Nahimovs, Raqueline A. M. Santos, Kamil Ravilevich Khadiev

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.

arXiv:1710.04046•Oct 11, 2017•0 citations

An improved algorithm for computing hitting probabilities of quantum walks

Yanbing Zhang, Tingting Song, Zhihao Wu

Physica A Statistical Mechanics and its Applications•Feb 2, 2022•1 citation

On the Probability of Finding Marked Connected Components Using Quantum Walks

Kamil Ravilevich Khadiev, Nikolajs Nahimovs, Raqueline A. M. Santos

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.

Lobachevskii Journal of Mathematics•Sep 1, 2018•5 citations

From quantum graphs to quantum random walks

Gregor Tanner

arXiv:quant-ph/0504224•Springer eBooks•Jun 25, 2006•20 citations

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

Adam Glos, Nikolay Nahimovs

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}.

arXiv:1907.12277•Jul 29, 2019•0 citations

The average search probabilities of discrete-time quantum walks

Hanmeng Zhan

arXiv:2108.09818•Quantum Information Processing•Sep 29, 2022•1 citation
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}.