A quantum computation problem of quantum search is discussed in this paper.Grover's search algorithm, the most commonly used quantum search algorithm, is introduced in details.The flow of quantum search algorithm and the quantum circuit model are shown.And the error of the search value, as well as the probability of measurement, is analyzed.For further research we simulated the Grover's search algorithm in classical computer.By quantum simulator the probability distribution of the measuring result of search value is presented and the computational efficiency is discussed.The simulation result demonstrates the effectiveness of the proposed algorithm.
A quantum computation problem of quantum search is discussed in this paper.Grover's search algorithm, the most commonly used quantum search algorithm, is introduced in details.The flow of quantum search algorithm and the quantum circuit model are shown.And the error of the search value, as well as the probability of measurement, is analyzed.For further research we simulated the Grover's search algorithm in classical computer.By quantum simulator the probability distribution of the measuring result of search value is presented and the computational efficiency is discussed.The simulation result demonstrates the effectiveness of the proposed algorithm.
This paper develops and analyzes Grover’s quantum search algorithm in 2- and 3-qubit systems in terms of the number of gates, representation of state vectors, and state vector measurement probabilities. We designed, verified and simulated the quantum circuit using QCAD. We present a theoretical implementation of the search algorithm in different qubit systems. We may observe that our circuit design for 2-qubit systems is accurate and does not allow any error when a small error occurs in the design of a 3-qubit quantum system. it was considered to what extend given information about object of the research is used purposefully in the modeling process, as a result of mathematical analysis of Grover’s method of the quantum algorithm, i.e. it is important to provide the adequacy of the model. The results of the optimization performed with the quantum algorithm based on Grover’s method are presented.
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.
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 research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms and the avenue of its application in multiple domains. Availability of efficient quantum simulators will enable the researchers to quickly verify their results and concepts in order to establish a working proof of correctness. One important algorithm that has become one of the basic ingredients to build other algorithms and models is the Grover's search Algorithm which is known to be the most compute intensive. Our approach highlights the design principles for the fast simulation of Grover's search which can be implemented on a general purpose personal computer. The performance obtained are encouraging when compared to the existing simulators.
At present, the scale of quantum computers in the real sense is still small, and quantum simulation has become one of the important ways of quantum theory research, grover quantum search algorithm is suitable for the search problem of disordered database. Firstly, according to the implementation principle of Grover algorithm and Boolean logic relationship, the design idea of multi-objective Oracle is analyzed, based on IBMQ quantum cloud platform, the quantum circuit of Grover algorithm with multi-objective items is simulated. Based on the characteristics of Grover algorithm and the simulation process of quantum gate, the action of multiple identical quantum gates is combined to reduce the update times of probability amplitude and improve the simulation efficiency. The libquantum quantum simulator is used for experiments and the target item is successfully searched, which proves the feasibility of the optimization method and provides reference for the simulation and optimization of other quantum algorithms.
Grover's search algorithm is one of the most significant quantum algorithms, which can obtain quadratic speedup of the extensive search problems. Since Grover's search algorithm cannot be implemented on a real quantum computer at present, its quantum simulation is regarded as an effective method to study the search performance. When simulating the Grover's algorithm, the storage space required is exponential, which makes it difficult to simulate the high-qubit Grover's algorithm. To this end, we deeply study the storage problem of probability amplitude, which is the core of the Grover simulation algorithm. We propose a novel memory-efficient method via amplitudes compression, and validate the effectiveness of the method by theoretical analysis and simulation experimentation. The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5% of the storage space than the uncompressed one. Thus under the same hardware conditions, our method can dramatically reduce the required computing nodes, and at the same time, it can simulate at least 3 qubits more than the uncompressed one. Particularly, our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.