This work tests the performance of Grover’s search circuits on some IBM superconducting quantum devices in case of the size of search space N = 16 and N = 32. Ideally, we expect to get an outcome probability distribution that is clearly peaked at the goal (marked) state. However, the quantum circuit executed on real devices is vulnerable to noise which leads to fluctuations in the results. The contributions of this paper are therefore the following: a) it presents two new Grover’s search circuits for N = 16 which were not yet reported in the state of the art; b) it shows performance difference between simulation results and results obtained on real devices; c) it shows the need of adding error correction on the circuit for N ≥ 32.
This work tests the performance of Grover’s search circuits on some IBM superconducting quantum devices in case of the size of search space N = 16 and N = 32. Ideally, we expect to get an outcome probability distribution that is clearly peaked at the goal (marked) state. However, the quantum circuit executed on real devices is vulnerable to noise which leads to fluctuations in the results. The contributions of this paper are therefore the following: a) it presents two new Grover’s search circuits for N = 16 which were not yet reported in the state of the art; b) it shows performance difference between simulation results and results obtained on real devices; c) it shows the need of adding error correction on the circuit for N ≥ 32.
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.
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.
In the context of actual information technology, data processing and storage have increased exponentially. Searching through large databases is considered an important problem, with multiple applications, where the properties of quantum computing could be used to find a potential solution. In this paper, the authors present an implementation for Grover’s search algorithm, a fast quantum algorithm for database search, and analyze the results for various graph topologies used in some of the real quantum devices provided by IBM. The algorithm provides a quadratic speedup over its classical counterpart (linear complexity). The code used in the implementation is possible with the help of the Qiskit framework and IBM Q Experience platform. Multiple tests with their results are presented. The experiments include three implementations of Grover’s search algorithm for different input register sizes: 2, 3 and 4 qubits, and exploration of multiple running configurations. We focus on the performance impact of selecting different groups of qubits on various real quantum devices, such as the probability to find the desired state and the execution time. For each experiment, we present the motivation, the results and their analysis.
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.
Unstructured searching, which is to find the marked element from a given unstructured data set, is a widely studied problem in computer science. It is well known that Grover algorithm provides a quadratic speedup to solve unstructured search problem compared with the classical algorithm. This algorithm has received a lot of attention due to the strong versatility. In this manuscript, we report experimental results of searching a unique target from 16 elements on five different quantum devices of IBM quantum Experience (IBMQ). We first implement the original Grover algorithm on these devices. However, the experiment probability of success of finding the correct target is almost the same as random choice. We then optimize the quantum circuit size of the search algorithm. The oracle operator and diffusion operator are two of the most costly operators in Grover algorithm. For the 16-element quantum search algorithm, both the oracle operator and diffusion operator consist of a triple controlled [Formula: see text] gate ([Formula: see text]) and some single-qubit gates. So we optimize the implementation of the [Formula: see text] gate according to the qubits layout of different quantum devices. On the ibmq_santiago, the experimental success rate of the 16-element quantum search algorithm is increased to [Formula: see text] by the optimization, which is better than all the published experiments implemented on IBMQ devices. For other IBMQ devices, the experimental success rate of 16-element quantum search also has been significantly improved. We then try to further reduce the size of the quantum circuit by modifying the Grover algorithm, with a tolerable loss of the theoretical success probability. On ibmq_quito, the experimental success rate is further improved from 25.23% to 27.56% after optimization. These experimental results show the importance of circuit optimization and algorithm optimization in the Noisy-Intermediate-Scale Quantum (NISQ) era.
This paper focuses on testing the current viability of using quantum computers for the processing of data-driven tasks fueled by emerging data science applications. We test the publicly available IBM quantum computers using Grover's algorithm, a well-known quantum search algorithm, to obtain a baseline for the general evaluations of these quantum devices and to investigate the impacts of various factors such as number of quantum bits (or qubits), qubit choice, and device choice. The main contributions of this paper include a new 4-qubit implementation of Grover's algorithm and test results showing the current capabilities of quantum computers. Our study indicates that quantum computers can currently only be used accurately for solving simple problems with very small amounts of data. There are also notable differences between different selections of the qubits in the implementation design and between different quantum devices that execute the algorithm.