Tensor Networks for Plasma Dynamics

Matrix product states (MPS) are widely used as a computational tool in the quantum physics community. However, it is believed that MPS can also potentially exponentially reduce the cost of numerical simulations of classical systems. Indeed, a few works have already used MPS or equivalent methods to solve multi-dimensional systems described by partial differential equations, such as those of fluids or large molecules, and reported significant computational savings. Here, we investigate the use of MPS to simulate a first-principles, kinetic description of plasmas, based on the (electrostatic or electromagnetic) Vlasov equation. Furthermore, we attempt to provide some additional insight on the MPS representation of this system and when the representation is efficient, which in turn can identify how quantum computers may be able assist these numerical simulations.