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:0811.4481

Strength and Weakness in Grover's Quantum Search Algorithm

Ahmed Younes

Published Nov 27, 2008• 17 citations
arXivHTMLPDF

Abstract

Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the database with quadratic speedup over the best known classical algorithm. This review paper discusses the performance of Grover's algorithm in case of multiple matches where the problem is expected to be easier. Unfortunately, we will find that the algorithm will fail for $M>3N/4$, where $M$ is the number of matches in the list.

DOI
10.48550/arxiv.0811.4481

Related papers

Comparison of Quantum and Classical Algorithm in Searching a Number in a Database Case

Zhiyao Wang

Contemporarily, quantum computing is one of the hottest research fields. Many quantum algorithms are proposed in order to utilize the power of quantum computers. Grover’s searching algorithm is one of them. In this article, by comparing a classical searching algorithm and Grover’s algorithm in the problem of finding a number in a finite database, the advantages of the latter are discussed. The actual quantum circuit to solve the problem is built and run on both a simulator and a real quantum computer. According to the analysis, Grover’s algorithm provides speedup in a searching task compared to the classical algorithm. However, noises in today’s quantum devices make the result of the quantum algorithm unreliable. In searching for multiple numbers, Grover’s algorithm has its shortcomings. Nevertheless, noises in quantum computing need to be addressed in order to utilize the potential of quantum computers in solving difficult problems. These results shed light on guiding further exploration of quantum algorithms and quantum computing.

Highlights in Science Engineering and Technology•Mar 16, 2023•2 citations

Improved quantum multi-object search algorithm

Wei-Yun Ma

Grover’s quantum mechanical search algorithm solves the unsorted database search with quadratic speed-up over the classical algorithms.But Grover’s algorithm will be inefficient when the number of matching is close to 2n/2.This paper presents a quantum algorithm which can get a target item with certainty by a single query when the number of the target items is more than a quarter.

Computer Engineering and Applications Journal•Jan 1, 2009•0 citations

Implementation of Database Search with Quantum Computing: Grover's Algorithm vs Linear Search

Sachin Khurana, Manisha J. Nene

The present study aims to examine the real-world implications of Grover's algorithm, specifically focusing on its quadratic speedup in contrast to classical linear search techniques employed for unsorted databases. The objective is to bridge the gap between theoretical potential and practical application in the field of quantum computing. This study conducts a comprehensive analysis of Grover's Algorithm and traditional linear search across databases of varying sizes, uniquely contributing by empirically validating Grover's Algorithm's superior performance and aligning it with theoretical expectations. Significantly, the study expands its analysis to encompass larger databases, further affirming the algorithm's utility in handling growing database sizes. This study significantly contributes to the progress of quantum computing through the practical implementation of theoretical principles as well as enhancing the scientific community's understanding of quantum search algorithms and their relative efficacy.

International Conference on Ambient Intelligence, Knowledge Informatics and Industrial Electronics (AIKIIE)•Nov 2, 2023•8 citations

Grover's Search Algorithm for Database Validation

Datapro Computers Pvt Ltd, Shravani Salapu

In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.

•Aug 11, 2026•0 citations

Grover's Search Algorithm for Database Validation

Dr CH Pavan Satish, K. Bhargavi, G.Vanaja +2 more

In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.

International Journal of Engineering Research and Science & Technology•Mar 22, 2026•0 citations

Quantum Search using Grover’s Algorithm: Principles, Performance, and Applications

Anggit Gusti Nugraheni, Heri Mahyuzar, Sri Hastuti

Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.

Asian journal of mathematics and computer research•Jun 23, 2026•0 citations
Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with NNN records in O(N)O(\sqrt{N})O(N​) assuming that the item must exist in the database with quadratic speedup over the best known classical algorithm. This review paper discusses the performance of Grover's algorithm in case of multiple matches where the problem is expected to be easier. Unfortunately, we will find that the algorithm will fail for M>3N/4M>3N/4M>3N/4, where MMM is the number of matches in the list.
Contemporarily, quantum computing is one of the hottest research fields. Many quantum algorithms are proposed in order to utilize the power of quantum computers. Grover’s searching algorithm is one of them. In this article, by comparing a classical searching algorithm and Grover’s algorithm in the problem of finding a number in a finite database, the advantages of the latter are discussed. The actual quantum circuit to solve the problem is built and run on both a simulator and a real quantum computer. According to the analysis, Grover’s algorithm provides speedup in a searching task compared to the classical algorithm. However, noises in today’s quantum devices make the result of the quantum algorithm unreliable. In searching for multiple numbers, Grover’s algorithm has its shortcomings. Nevertheless, noises in quantum computing need to be addressed in order to utilize the potential of quantum computers in solving difficult problems. These results shed light on guiding further exploration of quantum algorithms and quantum computing.
The present study aims to examine the real-world implications of Grover's algorithm, specifically focusing on its quadratic speedup in contrast to classical linear search techniques employed for unsorted databases. The objective is to bridge the gap between theoretical potential and practical application in the field of quantum computing. This study conducts a comprehensive analysis of Grover's Algorithm and traditional linear search across databases of varying sizes, uniquely contributing by empirically validating Grover's Algorithm's superior performance and aligning it with theoretical expectations. Significantly, the study expands its analysis to encompass larger databases, further affirming the algorithm's utility in handling growing database sizes. This study significantly contributes to the progress of quantum computing through the practical implementation of theoretical principles as well as enhancing the scientific community's understanding of quantum search algorithms and their relative efficacy.
In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.
In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.
Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.