Solving fractional differential equations on a quantum computer: A variational approach
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...
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sg-smu-ink.sis_research-100482024-07-25T07:52:38Z Solving fractional differential equations on a quantum computer: A variational approach LEONG, Fong Yew KOH, Dax Enshan KONG, Jian Feng GOH, Siong Thye KHOO, Jun Yong EWE, Wei Bin LI, Hongying THOMPSON, Jayne POLETTI, Dario 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. 2024-09-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/sis_research/9045 info:doi/10.1116/5.0202971 https://ink.library.smu.edu.sg/context/sis_research/article/10048/viewcontent/033802_1_5.0202971_pvoa_cc_by.pdf http://creativecommons.org/licenses/by/3.0/ Research Collection School Of Computing and Information Systems eng Institutional Knowledge at Singapore Management University Partial Differential Equations Theory and Algorithms |
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Partial Differential Equations Theory and Algorithms LEONG, Fong Yew KOH, Dax Enshan KONG, Jian Feng GOH, Siong Thye KHOO, Jun Yong EWE, Wei Bin LI, Hongying THOMPSON, Jayne POLETTI, Dario Solving fractional differential equations on a quantum computer: A variational approach |
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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. |
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author |
LEONG, Fong Yew KOH, Dax Enshan KONG, Jian Feng GOH, Siong Thye KHOO, Jun Yong EWE, Wei Bin LI, Hongying THOMPSON, Jayne POLETTI, Dario |
author_facet |
LEONG, Fong Yew KOH, Dax Enshan KONG, Jian Feng GOH, Siong Thye KHOO, Jun Yong EWE, Wei Bin LI, Hongying THOMPSON, Jayne POLETTI, Dario |
author_sort |
LEONG, Fong Yew |
title |
Solving fractional differential equations on a quantum computer: A variational approach |
title_short |
Solving fractional differential equations on a quantum computer: A variational approach |
title_full |
Solving fractional differential equations on a quantum computer: A variational approach |
title_fullStr |
Solving fractional differential equations on a quantum computer: A variational approach |
title_full_unstemmed |
Solving fractional differential equations on a quantum computer: A variational approach |
title_sort |
solving fractional differential equations on a quantum computer: a variational approach |
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Institutional Knowledge at Singapore Management University |
publishDate |
2024 |
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https://ink.library.smu.edu.sg/sis_research/9045 https://ink.library.smu.edu.sg/context/sis_research/article/10048/viewcontent/033802_1_5.0202971_pvoa_cc_by.pdf |
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