HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914112588480512 |
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| author | Liao, Shijun |
| author_facet | Liao, Shijun |
| contents | Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schrödingerisation [1,2,3]. In this paper, the Schrödingerisation technique for quantum simulation is expanded to ANY nonlinear PDEs by combining it with the homotopy analysis method (HAM). The HAM can transfer a nonlinear PDE into a series of linear PDEs with guaranteeing convergence of the series. In this way, ANY nonlinear PDEs can be solved by quantum simulation using a quantum computer. For simplicity, we call the procedure ``HAM-Schrödingerisation quantum algorithm''. Quantum computing is a groundbreaking technique. Hopefully, the ``HAM-Schrödingerisation quantum algorithm'' can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15821 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs Liao, Shijun Quantum Physics Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schrödingerisation [1,2,3]. In this paper, the Schrödingerisation technique for quantum simulation is expanded to ANY nonlinear PDEs by combining it with the homotopy analysis method (HAM). The HAM can transfer a nonlinear PDE into a series of linear PDEs with guaranteeing convergence of the series. In this way, ANY nonlinear PDEs can be solved by quantum simulation using a quantum computer. For simplicity, we call the procedure ``HAM-Schrödingerisation quantum algorithm''. Quantum computing is a groundbreaking technique. Hopefully, the ``HAM-Schrödingerisation quantum algorithm'' can open a door to highly efficient simulation of complicated turbulent flows by means of quantum computing in future. |
| title | HAM-Schrödingerisation: a generic framework of quantum simulation for any nonlinear PDEs |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.15821 |