Grover's quantum search algorithm, with a time complexity of , provides an efficient solution for searching unstructured databases. This study conducts a computational analysis of Grover's algorithm for quantum search in a geophysical database with (over one million) entries to identify a reservoir with a specific acoustic impedance (indicative of oil-bearing layers). Results demonstrate that with 804 iterations, a success probability of 99.999976% is achieved, offering approximately 652 times improvement over classical methods (averaging 524,288 checks). Sensitivity analysis confirms the algorithm's stability and scalability. Small-scale simulation in Cirq yields a 96.13% success probability, matching theoretical predictions exactly. This approach reduces geophysical data processing time from days to hours, potentially lowering oil exploration costs in Iran by up to 50% and addressing the need for efficient processing of large-scale seismic data. Grover's algorithm shows significant potential for oil reservoir exploration, overcoming limitations of traditional methods.
Grover's quantum search algorithm, with a time complexity of , provides an efficient solution for searching unstructured databases. This study conducts a computational analysis of Grover's algorithm for quantum search in a geophysical database with (over one million) entries to identify a reservoir with a specific acoustic impedance (indicative of oil-bearing layers). Results demonstrate that with 804 iterations, a success probability of 99.999976% is achieved, offering approximately 652 times improvement over classical methods (averaging 524,288 checks). Sensitivity analysis confirms the algorithm's stability and scalability. Small-scale simulation in Cirq yields a 96.13% success probability, matching theoretical predictions exactly. This approach reduces geophysical data processing time from days to hours, potentially lowering oil exploration costs in Iran by up to 50% and addressing the need for efficient processing of large-scale seismic data. Grover's algorithm shows significant potential for oil reservoir exploration, overcoming limitations of traditional methods.
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.
Now-a-days, the use of No-SQL databases is one of the potential options for storing and processing big data lakes. However, searching for large data in No-SQL databases is a complex and time-consuming task. Further, information retrieval from big data management suffers in terms of execution time. To reduce the execution time during the search process, we propose a fast and suitable approach based on the quantum Grover algorithm, which represents one of the best-known approaches for searching in an unstructured database and resolves the unsorted search query in O (√n) time complexity. To assess our proposal, a comparative study with linear and binary search algorithms was conducted to prove the effectiveness of Grover's algorithms. Then, we perform extensive experiment evaluations based on ibm_qasm_simulator for searching one item out of eight using Grover’s search algorithm based on three qubits. The experiments outcomes revealed encouraging results, with an accuracy of 0.948, well in accordance with the theoretical result. Moreover, a discussion of the sensitivity of Grover's algorithm through different iterations was carried out. Then, exceeding the optimal number of iterations round (π/4 √N), induces low accuracy of the marked state. Furthermore, the incorrect selection of this parameter can outline the solution.
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.
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.
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 algorithm was developed to solve the problem of searching an unstructured database for a certain unique element. In general, this problem can be formulated as follows: an unstructured database consists of elements and contains one unique element that has a certain property that can be tested with polynomial complexity, and which must be found with minimal time and complexity. Classical methods require querying the database to find the desired element, while Grover's algorithm allows you to perform only approximately steps, which are iterations of the procedure, to the database and be sure that the resulting element will be exactly the desired element with a probability close to 1. As in quantum algorithms aimed at cryptanalysis of symmetric transformations, Grover's algorithm repeats the procedure (Grover's iteration) to increase the probability of obtaining the correct result. Similarly to such algorithms in Grover's method, when iterations are continued after reaching the required number of iterations, the probability of obtaining the correct result decreases. This is due to the fact that during the execution of Grover's iteration, a rotation is performed in the complex space. Thus, each iteration, making a turn, brings the register closer and closer to the desired state, but at a certain point a maximum closeness is reached, at which the continued use of iterations will lead to a turn past the desired state, which will move the state of the system away from the desired state. The database for this algorithm can be any search space consisting of a certain number of elements. So, for example, it can be applied to find a secret key for a symmetric cryptograms formation or to find a collision for a hashing function.