Quantum computing of fluid dynamics using the hydrodynamic Schr¨odinger equation

Z. Meng, Y. Yang · 2023 · Phys. Rev. Research 5, 033182

| 编号 QC095 | 主题 量子格子玻尔兹曼 | 链接 10.1103/PhysRevResearch.5.033182 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Simulating fluid dynamics on a quantum computer is intrinsically dificult 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 threedimensional 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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