Quantum Computing for Computational Fluid Dynamics

如果不更好地了解流体动力学，我们今天面临的许多环境和能源相关问题就不可能得到解决。了解，预测和控制流体流动是至关重要的，也是一个限制因素，以广泛的行业：海军，航空，汽车，发电，过程，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，高性能计算技术取得了重大进展，计算流体动力学（CFD）已成为实验和理论的重要补充。虽然Navier-Stokes方程是描述湍流运动的一个被广泛接受的数学模型，但由于湍流的混沌性和固有的多尺度性，其解的获得非常具有挑战性。然而，即使使用当今最先进的算法和现代超级计算机，湍流的精确模拟也仅适用于一小类问题，即简单几何形状下的低速问题。由于此类模拟的计算成本很高，因此寻求高效的计算流体动力学算法仍然是一个悬而未决的问题。因此，探索和提供关于量子计算机算法应如何应用于解决计算流体力学问题的想法是很自然的。量子计算机基于量子力学现象，如叠加和纠缠来执行。由于量子演算法的运算方式是传统电脑无法做到的，因此量子演算法可以提供比传统演算法更快的运算速度。本计画将探讨量子演算法应用于计算流体力学问题的潜力。要执行的两个主要任务是：（1）确定经典流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（量子优势）带来的潜在计算增益，（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后端不可知的通用表达式，并在不同的分布式硬件后端上执行它们，而无需更改代码。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.