Journal of Electronics and Informatics
IRO Journals
Volume 6 — Issue 4 — December 2024

Quantum Speedup for Linear Systems: An Analysis of the HHL Algorithm Using IBM Qiskit

https://doi.org/10.36548/jei.2024.4.003
Shwetha V.
Department of Electronics Engineering, Madras Institute of Technology, Anna University, Chennai, India
Abinaya Selvarajan
Department of Electronics Engineering, Madras Institute of Technology, Anna University, Chennai, India
Aarthi A.
Department of Electronics Engineering, Madras Institute of Technology, Anna University, Chennai, India
Sneka R.
Department of Electronics Engineering, Madras Institute of Technology, Anna University, Chennai, India
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How to Cite

V., Shwetha, Abinaya Selvarajan, Aarthi A., and Sneka R. 2025. “Quantum Speedup for Linear Systems: An Analysis of the HHL Algorithm Using IBM Qiskit”. Journal of Electronics and Informatics 6 (4): 317-31. https://doi.org/10.36548/jei.2024.4.003.
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Keywords

— HHL Algorithm
— Quantum Computing
— Linear Systems of Equations
— Quantum Phase Estimation
— IBM Qiskit
— Noisy Intermediate-Scale Quantum Devices
— Fidelity Analysis
Published: 09-01-2025

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.

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