Leong, F. Y., Koh, D. E., Kong, J. F., Goh, S. T., Khoo, J. Y., Ewe, W.-B., Li, H., Thompson, J., & Poletti, D. (2024). Solving fractional differential equations on a quantum computer: A variational approach. AVS Quantum Science, 6(3). https://doi.org/10.1116/5.0202971
Abstract:
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering applications, such as the subdiffusion equation, the nonlinear Burgers' equation, and a coupled diffusive epidemic model. We assess quantum hardware performance under realistic noise conditions, further validating the practical utility of our algorithm.
License type:
Attribution 4.0 International (CC BY 4.0)
Funding Info:
This research / project is supported by the National Research Foundation - Quantum Engineering Programme
Grant Reference no. : NRF2021-QEP2-02-P03
This research / project is supported by the National Medical Research Council - Programme for Research in Epidemic Preparedness and Response
Grant Reference no. : PREPARE-CS1-2022-004
This research is supported by core funding from: Agency for Science, Technology and Research
Grant Reference no. : C23091700
This research / project is supported by the Agency for Science, Technology and Research - Central Research Fund (CRF) Award for Use-Inspired Basic Research
Grant Reference no. : NA
This research / project is supported by the Ministry of Education - Academic Research Fund Tier 2
Grant Reference no. : MOET2EP50120-0019
Description:
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Leong, F. Y., Koh, D. E., Kong, J. F., Goh, S. T., Khoo, J. Y., Ewe, W.-B., Li, H., Thompson, J., & Poletti, D. (2024). Solving fractional differential equations on a quantum computer: A variational approach. AVS Quantum Science, 6(3) and may be found at https://doi.org/10.1116/5.0202971