The Quantum Lattice Boltzmann Methods: Towards Quantum Methods for Computational Fluid Dynamics

There are certain computational problems that a quantum computer is expected to be able to solve more efficiently than a classical compute device. However, due to their specific structure and properties, quantum computers will not be beneficial for all types of computations. One potential use-case of interest is the so-called lattice Boltzmann method, which is a computational approach that can be used to model the flow of fluid. The lattice Boltzmann method models fluid flow by dividing the process into its two natural steps of streaming and collision and simulating them separately. This means that the method is naturally split up into a linear and a local step, this structure is potentially interesting for quantum computers as they portray naturally linear behavior and local computations can be done in parallel. The aim of this thesis is to determine how quantum computers could be used to implement a quantum Lattice Boltzmann method and if such an implementation would constitute a speed-up over classical methods. In Chapter 1 we give a brief introduction to quantum computing, computational fluid dynamics (CFD), the Boltzmann method and the field of quantum CFD....