H-DES: a Quantum-Classical Hybrid Differential Equation Solver
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arXiv
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| Format: | Preprint |
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2024
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| author | Jaffali, Hamza de Araujo, Jonas Bastos Milazzo, Nadia Reina, Marta de Boutray, Henri Baumann, Karla Holweck, Frédéric Mohdeb, Youcef Katz, Roland |
| author_facet | Jaffali, Hamza de Araujo, Jonas Bastos Milazzo, Nadia Reina, Marta de Boutray, Henri Baumann, Karla Holweck, Frédéric Mohdeb, Youcef Katz, Roland |
| contents | In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions that are encoded directly in the quantum states generated by different parametrized circuits, and transforms the task of solving the differential equations into an optimization problem. We first describe the principle of the algorithm from a theoretical point of view. We provide a detailed pseudo-code of the algorithm, on which we elaborate preliminary elements for a complexity analysis to highlight some of its scaling properties. We apply our algorithm to a set of examples, running on emulators and real hardware showcasing its applicability across diverse sets of differential equations. We discuss the advantages of our method and potential avenues for further exploration and refinement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | H-DES: a Quantum-Classical Hybrid Differential Equation Solver Jaffali, Hamza de Araujo, Jonas Bastos Milazzo, Nadia Reina, Marta de Boutray, Henri Baumann, Karla Holweck, Frédéric Mohdeb, Youcef Katz, Roland Quantum Physics Numerical Analysis Analysis of PDEs Optimization and Control In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions that are encoded directly in the quantum states generated by different parametrized circuits, and transforms the task of solving the differential equations into an optimization problem. We first describe the principle of the algorithm from a theoretical point of view. We provide a detailed pseudo-code of the algorithm, on which we elaborate preliminary elements for a complexity analysis to highlight some of its scaling properties. We apply our algorithm to a set of examples, running on emulators and real hardware showcasing its applicability across diverse sets of differential equations. We discuss the advantages of our method and potential avenues for further exploration and refinement. |
| title | H-DES: a Quantum-Classical Hybrid Differential Equation Solver |
| topic | Quantum Physics Numerical Analysis Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2410.01130 |