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Home / Archives / Volume-6 / Issue-4 / Article-3

Volume - 6 | Issue - 4 | december 2024

Quantum Speedup for Linear Systems: An Analysis of the HHL Algorithm Using IBM Qiskit Open Access
Shwetha V.  , Abinaya Selvarajan, Aarthi A., Sneka R.  397
Pages: 317-331
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Cite this article
V., Shwetha, Abinaya Selvarajan, Aarthi A., and Sneka R.. "Quantum Speedup for Linear Systems: An Analysis of the HHL Algorithm Using IBM Qiskit." Journal of Electronics and Informatics 6, no. 4 (2024): 317-331
Published
09 January, 2025
Abstract

One of the most significant developments in quantum computing is the Harrow-Hassidim-Lloyd (HHL) method, which can solve linear equation systems at exponential speedup. Because linear systems are essential to many scientific fields, including physics, engineering, and machine learning, this approach has great potential to revolutionize computational paradigms. The HHL algorithm is thoroughly examined in this work, with particular attention paid to its theoretical framework, real-world application utilizing IBM's Qiskit platform, and the difficulties in simulating quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. Using parameters like fidelity, time complexity, and scalability, the research further evaluates the HHL algorithm's performance in comparison to traditional methods. According to the findings, quantum simulations work well for small-scale matrices like 2x2 and 4x4, but expanding the approach to bigger systems is still difficult because of hardware and software constraints. Finally, the research emphasizes the key directions for advancing quantum hardware and algorithms to overcome current scalability challenges, enabling broader applicability of the HHL algorithm in solving complex linear systems.

Keywords

HHL Algorithm Quantum Computing Linear Systems of Equations Quantum Phase Estimation IBM Qiskit Noisy Intermediate-Scale Quantum Devices Fidelity Analysis

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