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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.09741 |
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| _version_ | 1866916080513974272 |
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| author | Meng, Zhaoyuan Yang, Yue |
| author_facet | Meng, Zhaoyuan Yang, Yue |
| contents | Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schrödinger equation (HSE), which can be promising in simulating three-dimensional turbulent flows in various engineering applications. The HSE is derived by generalizing the Madelung transform to compressible/incompressible flows with finite vorticity and dissipation. Since the HSE is expressed as a unitary operator on a two-component wave function, it is more suitable than the NSE for quantum computing. The flow governed by the HSE can resemble a turbulent flow consisting of tangled vortex tubes with the five-thirds scaling of energy spectrum. We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with exponential speedup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09741 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation Meng, Zhaoyuan Yang, Yue Fluid Dynamics Quantum Physics Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schrödinger equation (HSE), which can be promising in simulating three-dimensional turbulent flows in various engineering applications. The HSE is derived by generalizing the Madelung transform to compressible/incompressible flows with finite vorticity and dissipation. Since the HSE is expressed as a unitary operator on a two-component wave function, it is more suitable than the NSE for quantum computing. The flow governed by the HSE can resemble a turbulent flow consisting of tangled vortex tubes with the five-thirds scaling of energy spectrum. We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with exponential speedup. |
| title | Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation |
| topic | Fluid Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2302.09741 |