Quantum Computing for Computational Fluid Dynamics

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.