Quantum Machine Learning for Computational Fluid Dynamics

Recently there has been increased interest within the computational physics community in the study of neural ODE solvers, which use neural networks to attempt to find simpler solutions for systems of linear or non-linear ordinary differential equations. In this talk, I will discuss the role that quantum machine learning could play in this space and show the advantages as well as disadvantages of such algorithms. Speciifcally, I will discuss various flavors of quantum neural networks and show how quantum computers can be used to train them given classical data. I will then present a no-go result, showing that non-linear differential equations that support chaotic dynamics cannot be directly solved using the most popular approaches and suggest new approaches to linearize the dynamics that may be more profitable for neural quantum ODEs as well as quantum algorithms based on the linear-system solver of Harrow Hassidim and Lloyd.