Abstract Quantum computing can solve some classes of problems faster than classical computing. Among the greatest quantum algorithms to showcase this benefit is Grover's search algorithm, which has a quadratic speed-up for unstructured search problems. In this study, we present an implementation of Grover’s algorithm on a large-scale dataset comprising approximately 131,072 (217) names. We contrast its efficiency with the classical linear search based on time complexity, scalability, and the likelihood of success. The experiment was conducted using Qiskit on a quantum simulator, where several query scenarios were implemented to verify the algorithm's efficiency and accuracy. Our findings highlight the theoretical advantage of Grover’s algorithm in situations involving large data sets, while also discussing real-world limitations such as gate noise, qubit number, and circuit depth as we move towards actual quantum hardware. This study serves as a step toward evaluating the real-world relevance of quantum search algorithms and provides information on current challenges and future directions in quantum information retrieval.
Abstract Quantum computing can solve some classes of problems faster than classical computing. Among the greatest quantum algorithms to showcase this benefit is Grover's search algorithm, which has a quadratic speed-up for unstructured search problems. In this study, we present an implementation of Grover’s algorithm on a large-scale dataset comprising approximately 131,072 (217) names. We contrast its efficiency with the classical linear search based on time complexity, scalability, and the likelihood of success. The experiment was conducted using Qiskit on a quantum simulator, where several query scenarios were implemented to verify the algorithm's efficiency and accuracy. Our findings highlight the theoretical advantage of Grover’s algorithm in situations involving large data sets, while also discussing real-world limitations such as gate noise, qubit number, and circuit depth as we move towards actual quantum hardware. This study serves as a step toward evaluating the real-world relevance of quantum search algorithms and provides information on current challenges and future directions in quantum information retrieval.
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.
Target item searching in large-scale, unstructured text databases is a major computational task for traditional systems and usually requires algorithms whose time complexity is on the order ofO(N). Quantum computing presents a strong competitor by using Grover's algorithm, where theoretically the search complexity comes down toO(N), making faster retrieval possible. This research considers the design and assessment of Grover's algorithm as it is used to find a target word in a paragraph. The process entails encoding a group of unique words into a quantum register and implementing a circuit that incorporates a bespoke oracle and a diffusion operator to amplify the probability amplitude of the target state. Performance was evaluated in two situations: an ideal noise-free simulation with Qiskit's AerSimulator and a real-world run on IBM's quantum hardware. Simulation results demonstrated always-high accuracy in identifying the target word. But tests on real quantum machines indicated that the reliability of the algorithm decreases with an increase in qubits. Though circuits of up to five qubits had tolerable accuracy, larger configurations were plagued by noise, gate errors, and decoherence effects. These results highlight both the potential of quantum search algorithms for text processing and the limitations of NISQ today.
Quantum computing is on the cusp of transforming the way we tackle complex problems, and the Grover search algorithm exemplifying its potential to revolutionize the search for unstructured large datasets, offering remarkable speedups over classical methods. Here, we report results for the implementation and characterization of a three-qubit Grover search algorithm using the state-of-the-art scalable quantum computing technology of superconducting quantum architectures. To delve into the algorithm's scalability and performance metrics, our investigation spans the execution of the algorithm across all eight conceivable single-result oracles, alongside nine two-result oracles, employing IBM Quantum's 127-qubit quantum computers. Moreover, we conduct five quantum state tomography experiments to precisely gauge the behavior and efficiency of our implemented algorithm under diverse conditions - ranging from noisy, noise-free environments to the complexities of real-world quantum hardware. By connecting theoretical concepts with real-world experiments, this study not only shed light on the potential of Noisy Intermediate-Scale Quantum Computers in facilitating large-scale database searches but also offer valuable insights into the practical application of the Grover search algorithm in real-world quantum computing applications.
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.
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.