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Algorithms
Volume 18
Issue 8
10.3390/a18080491
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

by
Muqing Zheng
*,
Chenxu Liu
,
Samuel Stein
,
Xiangyu Li
,
Johannes Mülmenstädt
,
Yousu Chen
and
Ang Li
*
Pacific Northwest National Laboratory, Richland, WA 99354, USA
*
Authors to whom correspondence should be addressed.
Algorithms 2025, 18(8), 491; https://doi.org/10.3390/a18080491
Submission received: 8 July 2025 / Revised: 3 August 2025 / Accepted: 5 August 2025 / Published: 6 August 2025
(This article belongs to the Special Issue Algorithms for Quantum Computing and Quantum-Centric High-Performance Computing)
Versions Notes

Abstract

In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.
Keywords: quantum computing; quantum simulation; hybrid software for QC-HPC quantum computing; quantum simulation; hybrid software for QC-HPC

Share and Cite

MDPI and ACS Style

Zheng, M.; Liu, C.; Stein, S.; Li, X.; Mülmenstädt, J.; Chen, Y.; Li, A. An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications. Algorithms 2025, 18, 491. https://doi.org/10.3390/a18080491

AMA Style

Zheng M, Liu C, Stein S, Li X, Mülmenstädt J, Chen Y, Li A. An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications. Algorithms. 2025; 18(8):491. https://doi.org/10.3390/a18080491

Chicago/Turabian Style

Zheng, Muqing, Chenxu Liu, Samuel Stein, Xiangyu Li, Johannes Mülmenstädt, Yousu Chen, and Ang Li. 2025. "An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications" Algorithms 18, no. 8: 491. https://doi.org/10.3390/a18080491

APA Style

Zheng, M., Liu, C., Stein, S., Li, X., Mülmenstädt, J., Chen, Y., & Li, A. (2025). An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications. Algorithms, 18(8), 491. https://doi.org/10.3390/a18080491

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