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.
Zheng, Muqing, et al. "An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications." Algorithms, vol. 18, no. 8, Aug. 2025. https://doi.org/10.3390/a18080491
Zheng, Muqing, Liu, Chenxu, Stein, Samuel, Li, Xiangyu, Mülmenstädt, Johannes, Chen, Yousu, & Li, Ang (2025). An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications. Algorithms, 18(8). https://doi.org/10.3390/a18080491
Zheng, Muqing, Liu, Chenxu, Stein, Samuel, et al., "An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications," Algorithms 18, no. 8 (2025), https://doi.org/10.3390/a18080491
@article{osti_2587779,
author = {Zheng, Muqing and Liu, Chenxu and Stein, Samuel and Li, Xiangyu and Mülmenstädt, Johannes and Chen, Yousu and Li, Ang},
title = {An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications},
annote = {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.},
doi = {10.3390/a18080491},
url = {https://www.osti.gov/biblio/2587779},
journal = {Algorithms},
issn = {ISSN 1999-4893},
number = {8},
volume = {18},
place = {United States},
publisher = {MDPI AG},
year = {2025},
month = {08}}
Proceedings of the SC '23 Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysishttps://doi.org/10.1145/3624062.3624211