使用流体动力学薛定谔方程进行流体动力学的量子计算
Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation
AI总结：
提出基于流体动力学薛定谔方程的量子计算框架，通过推广Madelung变换处理可压缩/不可压缩流动，并开发预测-校正量子算法在Qiskit上实现指数级加速。
摘要：
由于Navier-Stokes equation（NSE）的非线性和非哈密顿性质，在量子计算机上模拟流体动力学本质上很困难。我们提出了一个基于hydrodynamic Schrödinger equation（HSE）的流体动力学量子计算框架，该框架在模拟各种工程应用中的三维湍流方面具有前景。HSE通过将Madelung变换推广到具有有限涡度和耗散的可压缩/不可压缩流动中导出。由于HSE被表示为双分量波函数上的酉算子，它比NSE更适合量子计算。由HSE控制的流动可以类似于由缠结涡管组成的湍流，其能谱具有三分之二的标度。我们开发了一种预测-校正量子算法来求解HSE。该算法在量子模拟器Qiskit上实现简单流动，具有指数级加速。
英文摘要：
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.
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