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.
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.
In this paper, we design and analyse the Circuit for Grover’s Quantum Search Algorithm on 2, 3 and 4-qubit systems, in terms of number of gates, representation of state vectors and measurement probability for the state vectors. We designed, examined and simulated the quantum circuit on IBM Q platform using Quantum Programming Studio. We present the theoretical implementation of the search algorithm on different qubit systems. We observe that our circuit design for 2 and 4-qubit systems are precise and do not introduce any error while experiencing a small error to our design of 3-qubit quantum system.
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.
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.
Models of Grover’s search algorithm is reviewed to build the foundation for the other algorithms. Thereafter, some preliminary modifications of the original algorithms by others are stated, that increases the applicability of the search procedure. A general quantum computation on an isolated system can be represented by a unitary matrix. In order to execute such a computation on a quantum computer, it is common to decompose the unitary into a quantum circuit, i.e., a sequence of quantum gates that can be physically implemented on a given architecture. There are different universal gate sets for quantum computation. Here we choose the universal gate set consisting of CNOT and single-qubit gates. We measure the cost of a circuit by the number of CNOT gates as they are usually more difficult to implement than single qubit gates and since the number of single-qubit gates is bounded by about twice the number of CNOT’s.
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 search algorithms have important applications in quantum information, which have been experimentally demonstrated in several quantum systems with database sizes up to 16. We first propose an efficient quantum search scheme based on an optimized Grover’s algorithm and a novel encoding method. With this scheme, a target element can be deterministically searched in a large database using only a single qubit. Then we implement this search scheme in linear optics with database sizes up to 40. Experimental results fit well with the theoretical results, with all fidelities greater than 99.7%. The limitation of the number of elements encoded in a single qubit is also investigated in the experiment. The experimental results indicate that a target state can be successfully searched from a database of size 36 using a single qubit in our laboratory. Since only one qubit and one-qubit gates are required, this search scheme is quite efficient and general, and can be adopted to implement the same task in most quantum systems.