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Herald of Omsk University

Realization of the Grover algorithm with error correction

E. A. Shafeev, Andrey N. Vakilov

Published Jan 1, 2024• 0 citations
Publisher

Abstract

A quantum Grover search algorithm has been implemented using the Qiskit software development kit and the IBM Quantum Lab. The accuracy of the algorithm is analyzed depending on the number of qubits. The Shore code for error correction is implemented.
DOI
10.24147/1812-3996.2024.2.21-26

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This paper provides an introduction to a quantum search algorithm, known as Grover’s Algorithm, for unsorted search purposes. The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK by IBM. While providing detailed proof, the computational complexity of the algorithm is generalized to n qubits. The implementation results obtained from the IBM QASM Simulator and IBMQ Santiago quantum backend are analyzed and compared. Finally, the paper discusses the challenges faced in implementation and real-life applications of the algorithm hitherto. Overall, the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.
With the growth of quantum computing hardware technology, more developers are becoming involved in the design and development of quantum algorithms, leading to the creation of practical applications that align with real-world needs through the combination of quantum hardware and software. Among quantum algorithms, the most well-known include Grover’s algorithm and Shor’s algorithm. Grover’s algorithm can quickly provide search results, making it highly valuable for search-related applications. In light of this, this study primarily examines the theoretical usability of Grover’s algorithm and explores its limitations. Additionally, on the practical side, this research implements Grover’s algorithm using IBM Quantum Computing and the IBM Qiskit package. By comparing simulation results with those obtained from execution on real quantum computers, the study discusses the current limitations of quantum computing hardware technology.