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

Lecture notes in networks and systems

Simulation-Based Comparison of Classical Linear Search and Grover’s Quantum Algorithm

Tsvetelina Stefanova, Tsvetozar Stefanov Georgiev

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-24810-7_15

Related papers

A Comprehensive Analysis of Grover's Search Quantum Algorithm in Qiskit Simulator

Varun Barthwal, Aditya Raj Thakur, Pradeep Rana

Grover's algorithm, which was discovered in 1996, is faster than any classical algorithm can ever be. Quantum systems are in a superposition of states and can examine multiple data simultaneously. This work conducted a comprehensive analysis to understand how Grover's algorithm works. Grover's search provides quadratic speed in comparison to the classical one; it explores target data in the unstructured database. Grover search starts with the superposition of all Qubits, which results in the same amplitude for all data points. To achieve superposition, the Hadamard gate was applied to all Qubits. Further, a black box function named Oracle is applied to mark the desired state. In the next phase, amplitude amplification is done, which enhances the probability of the desired data point. Thus, Grover's search yields results with an O (√ N) complexity, while its counterpart classical algorithm searches the desired data point with an O (N) complexity. Experiments have been performed on the Qiskit simulator using 2 and 3 qubits for the detailed analysis of Grover's search.

Advances in computational intelligence and robotics book series•May 13, 2025•0 citations

Analysis of Grover’S Quantum Search Algorithm on a Classical Computer

Necati Çeli̇k, Özkan Bingöl

•Jan 1, 2022•0 citations

Classical vs Quantum Search: Experimental Performance Analysis of Grover's Algorithm on Real IBM Quantum Hardware

Kundan Kumar Sahu

Grover's quantum search algorithm provides a proven quadratic speedup over classical linear search for unstructured databases. While its theoretical advantage is well established, experimental validation on real noisy intermediate-scale quantum (NISQ) hardware remains limited by noise, decoherence, and hardware constraints. In this work, we present an experimental comparison between classical linear search and Grover's quantum search algorithm executed on IBM Quantum real superconducting hardware using Qiskit Runtime. A four-qubit implementation corresponding to a 16-element search space is evaluated across multiple experimental runs. The results demonstrate consistent amplitude amplification, achieving an average success probability of 54.25% and an amplification factor of 8.68× over random guessing. Although classical execution remains faster in wall-clock time due to quantum hardware overhead, the experiment empirically validates the algorithmic advantage of Grover's search and quantifies the performance gap between ideal and real quantum processors in the NISQ era.

•Dec 29, 2025•1 citation

Deterministic Application of Grover’s Quantum Search Algorithm

Kyoichi Okamoto, Osamu Watanabe

Lecture notes in computer science•Jan 1, 2001•1 citation

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

Trimming Grover's Quantum Search Algorithm

Grant Eberle, Gonzalo E. Ordonez

Bulletin of the American Physical Society•Mar 2, 2020•0 citations
Grover's algorithm, which was discovered in 1996, is faster than any classical algorithm can ever be. Quantum systems are in a superposition of states and can examine multiple data simultaneously. This work conducted a comprehensive analysis to understand how Grover's algorithm works. Grover's search provides quadratic speed in comparison to the classical one; it explores target data in the unstructured database. Grover search starts with the superposition of all Qubits, which results in the same amplitude for all data points. To achieve superposition, the Hadamard gate was applied to all Qubits. Further, a black box function named Oracle is applied to mark the desired state. In the next phase, amplitude amplification is done, which enhances the probability of the desired data point. Thus, Grover's search yields results with an O (√ N) complexity, while its counterpart classical algorithm searches the desired data point with an O (N) complexity. Experiments have been performed on the Qiskit simulator using 2 and 3 qubits for the detailed analysis of Grover's search.
Grover's quantum search algorithm provides a proven quadratic speedup over classical linear search for unstructured databases. While its theoretical advantage is well established, experimental validation on real noisy intermediate-scale quantum (NISQ) hardware remains limited by noise, decoherence, and hardware constraints. In this work, we present an experimental comparison between classical linear search and Grover's quantum search algorithm executed on IBM Quantum real superconducting hardware using Qiskit Runtime. A four-qubit implementation corresponding to a 16-element search space is evaluated across multiple experimental runs. The results demonstrate consistent amplitude amplification, achieving an average success probability of 54.25% and an amplification factor of 8.68× over random guessing. Although classical execution remains faster in wall-clock time due to quantum hardware overhead, the experiment empirically validates the algorithmic advantage of Grover's search and quantifies the performance gap between ideal and real quantum processors in the NISQ era.
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.