Can quantum algorithms revolutionise the simulation of turbulent flows?

我们的研究愿景是创建一个框架和工具箱，将60多年的高性能计算与量子计算结合起来，以彻底改变对流体力学的理解、建模和模拟。风力发电场中能量的高效转换、超新星的爆炸以及飞机周围的空气阻力都有一个共同的因素：流体。流体力学是英国工业和研究的主要优势，是运输、医疗保健、海洋和能源领域的一项使能技术。根据2021年英国白皮书，流体力学是一个在2200家公司雇佣4.5万名员工的行业，为英国创造了140亿GB的产出。有实际意义的流体可能是湍急的。无论在基础研究还是应用研究中，数值模拟都是理解、预测和控制湍流流动的关键。在基础研究中，目标是揭示湍流的物理机制、尺度和动力学。在工业中，目标是将准确的湍流数值模拟快速地嵌入到工程设计周期中。虽然我们知道有一个很好的湍流模型(Navier-Stokes方程)，但湍流的混沌性质使得精确的计算机模拟变得极其昂贵。例如，对简单槽道水流进行最先进的湍流模拟需要3500亿个网格点，需要2.6亿个计算小时。为了分析基本和工程配置，部署了大量超级计算资源。尽管计算机的翻转操作大约每两年翻一番，但我们需要等待几十年才能以真实的流动速度处理基本的流动，如渠道流动。然而，与最先进的计算机相比，下一代大型艾级计算机只能将流动速度提高三到五倍。问题是“我们如何才能用负担得起的计算方法准确地模拟有实际意义的湍流？”经典算法正在达到它们的极限。这一建议的关键是观察到湍流非线性方程的数值解围绕着求解线性系统。用量子算法可以以惊人的速度解线性系统。量子计算提供了一个算法储存库，可以彻底改变计算科学和湍流模拟。这是因为经典计算机需要随系统自由度呈指数级增长的计算资源，而量子算法只按多项式增长。这也被称为量子优势。如果谷歌、微软、IBM、麻省理工学院、哈佛等人在2021年发表的关于量子优势的猜测是正确的，那么湍流系统的模拟可以加速一万到几千个数量级。该项目将开创这一研究领域的先河。在这个项目中，我们将开发和测试量子增强计算流体动力学(Q-CFD)，利用未经测试但看似合理的量子优势。这将为使用经典算法和量子算法的协同组合计算湍流开辟道路。

Our research vision is to create a framework and toolbox to marry over 60 years of high-performance computing with quantum computing to revolutionise understanding, modelling, and simulation of fluid mechanics. The efficient conversion of energy in wind farms, the explosions of supernovas, and the air resistance around airplanes have a common factor: a fluid. Fluid mechanics is a major UK industrial and research strength, which is an enabling technology from transport, healthcare, marine and energy. According to the 2021 UK white paper, fluid mechanics is a sector that employs 45,000 people in 2,200 companies, which generates a £14-billion output to the UK. Fluids of practical interest can be turbulent. Both in fundamental and applied research, numerical simulation is key to understanding, predicting and controlling turbulent flows. In fundamental research, the goal is to unveil the physical mechanisms, scales and dynamics of turbulence. In industry, the goal is to embed accurate numerical simulations of turbulence with a fast turnaround into the engineering design cycle. We are far from achieving this.Although we know an excellent model for turbulent flows (the Navier-Stokes equations), the chaotic nature of turbulence makes accurate computer simulations exceedingly expensive. For example, a state-of-the-art simulation of turbulence of a simple channel flow needs 350 billion grid points and takes 260 million computing hours. To analyse fundamental and engineering configurations, large supercomputing resources are deployed. Although the flop operations of computers roughly double every two years, we will need to wait for decades before being able to tackle a fundamental flow, such as a channel flow, at realistic flow velocities. The next generation of large exascale computers, however, will only allow for a three- to five-fold increase in the flow velocities with respect to the state-of-the-art. The question is "how can we accurately simulate turbulent flows of practical interest with affordable computations?" Classical algorithms are reaching their limits.Key to this proposal is the observation that the numerical solution of the nonlinear equations of turbulence revolves around solving linear systems. Linear systems can be solved formidably fast by quantum algorithms. Quantum computing offers a repository of algorithms that can revolutionise computational science and turbulence simulations. This is because classical computers require computational resources that scale exponentially with the system's degrees of freedom, whereas quantum algorithms scale only polynomially. This is also known as the quantum advantage. If the conjectures published in 2021 by Google, Microsoft, IBM, MIT, Harvard, among others, on the quantum advantage are correct, the simulation of a turbulent system can be accelerated by ten to thousand orders of magnitudes. This project will pioneer this research field. In this project, we will develop and test quantum-enhanced computational fluid dynamics (q-CFD) by exploiting the untested, but plausible, quantum advantage. This will blaze the trail for computing turbulence with a synergistic combination of classical and quantum algorithms.