Quantum Computing for Computational Fluid Dynamics

如果不能更好地了解流体的动力学，我们今天面临的许多与环境和能源有关的问题都不可能得到解决。了解、预测和控制流体流动对于许多行业都是至关重要的，也是一个限制因素：海军、航空、汽车、发电、工艺、制药、气象、环境等。模拟和了解流体流动是科学中最具挑战性的问题之一。近年来，高性能计算取得了显著的进展，计算流体力学是对实验和理论的重要补充。虽然Navier-Stokes方程构成了一个被广泛接受的描述湍流运动的数学模型，但由于湍流的混沌和固有的多尺度性质，其解的获得可能是极其困难的。然而，即使有了今天最先进的算法和现代的超级计算机，对湍流的准确模拟也只适用于一小类问题，在简单的几何图形中以低速运行。由于这种模拟的计算成本很高，因此对高效计算流体动力学算法的探索仍然是一个悬而未决的问题。因此，探索和提供关于如何将量子计算机算法应用于求解计算流体动力学问题的想法是很自然的。量子计算机是基于叠加和纠缠等量子力学现象来执行的。因为量子算法的计算方式是经典计算机无法实现的，所以量子算法可以提供比经典算法更快的速度。本项目将研究量子计算机算法在计算流体动力学问题中的应用潜力。要执行的两项主要任务是：(1)确定经典流动求解器的哪些部分可以被量子计算机算法取代，考虑到该算法相对于标准算法将带来的潜在计算收益(量子优势)，(2)通过轻量级表达式模板库(参见LibKet库作为原始示例)开发、测试和验证此类算法。这个想法是提出量子算法作为与后端无关的通用表达式，并在不同的分布式硬件后端上执行它们，而不需要更改代码。这样的库将使以抽象的方式制定量子算法成为可能，而不是使用针对特定语言和量子硬件的低级量子门来表达量子算法。

Many of the environmental and energy-related issues we face today cannot possibly be tackled without a better understanding of the dynamics of fluids. Understanding, predicting and controlling fluid flows is of central importance and a limiting factor to a vast range of industries:naval, aeronautical, automotive, power generation, process, pharmaceutical, meteorological, environmental, etc. Simulating and understanding fluid flows is one of the most challenging problems in science. Significant progress has been made recently using High Performance Computing, and Computational Fluid Dynamics is now a critical complement to experiments and theories.While the Navier-Stokes equations constitute a broadly accepted mathematical model to describe the motions of a turbulent flow, their solutions can be extremely challenging to obtain due to the chaotic and inherently multi-scale nature of turbulence. However, even with today's state-of-the-art algorithms and modern supercomputers, accurate simulations of turbulent flows are only feasible for a small class of problems, at low speeds in simple geometries.As such simulations are computationally expensive, the quest of highly efficient Computational Fluid Dynamics algorithms remains an open question for the community. It is therefore natural to explore and provide ideas about how quantum computers algorithms should be applied to solving Computational Fluid Dynamics problems.Quantum computers are based on quantum mechanical phenomena such as superposition and entanglement to perform. Because they compute in ways that classical computers cannot, quantum algorithms can provide exponential speedups over their classical counterparts.This project will investigate the potential of quantum computers algorithms applied to Computational Fluid Dynamics problems. The two main tasks to be carried out are: (1) Identify which parts of a classical flow solver can be replaced by quantum computers algorithms, taking into account the potential computational gains that the algorithm would bring with respect to the standard algorithm (quantum advantage), (2) develop, test and validate such algorithms, via a lightweight expression template library (see the LibKet library as a primitive example). The idea is to propose quantum algorithms as backend-agnostic generic expressions and execute them on different distributed hardware backends without changing the code. Such library will make it possible to formulate quantum algorithms in an abstract way, as opposed to express quantum algorithms using low-level quantum gates for a particular language and quantum hardware.