2023/02/20 by Zhaoyuan Meng, Yue Yang · 1 voice
Computer Science · Mathematics · Physics and Astronomy · #Barotropic fluid #Classical mechanics #Fluid dynamics #Hamiltonian (control theory) #Mathematical optimization #Mathematics #Mechanics #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum fluid #Quantum mechanics #Statistical physics #Vortex #Vorticity #Vorticity equation #physics.flu-dyn #quant-ph
paper · pdf · doi:10.1103/physrevresearch.5.033182
arxiv published 2023/02/20 · arxiv updated 2023/02/20 · openalex publication_date 2023/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 or 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 partial exponential speedup.