Quantum computing of fluid dynamics using the hydrodynamic Schr\"odinger equation

• URL: http://arxiv.org/abs/2302.09741v1
• Date: Mon, 20 Feb 2023 03:43:27 GMT
• Title: Quantum computing of fluid dynamics using the hydrodynamic Schr\"odinger equation
• Authors: Zhaoyuan Meng and Yue Yang
• Abstract summary: We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schr"odinger equation (HSE) 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.
• Score: 7.752417113600681
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Schr\"odinger 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.

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