Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach

• URL: http://arxiv.org/abs/2406.08755v1
• Date: Thu, 13 Jun 2024 02:27:16 GMT
• Title: Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach
• Authors: Fong Yew Leong, Dax Enshan Koh, Jian Feng Kong, Siong Thye Goh, Jun Yong Khoo, Wei-Bin Ewe, Hongying Li, Jayne Thompson, Dario Poletti,
• Abstract summary: We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation cost scales economically with the number of time steps.
• Score: 0.1492582382799606
• License: http://creativecommons.org/licenses/by/4.0/
• 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 time complexity, but has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation cost scales 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 sub-diffusion equation, the non-linear 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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