Quantum Computing applied to Partial Differential Equations in Plasma Physics

Abstract:
Quantum computers are a promising tool to solve certain problems that are out of reach of classical computers. In this presentation, I propose new quantum algorithms for solving some nonlinear partial differential equations, which occur frequently in the context of plasma physics.

I start by presenting new classical methods with better asymptotic complexity, and then prove that, when compared with the classical case, this new quantum algorithm shows an exponential speedup with regards to the number of time steps considered, while also having a quadratic speedup in other parameters. Additionally, I also propose a new techniques to perform quantum error correction and to study quantum many-body systems.