A quantum-inspired method for solving the Vlasov-Poisson equations

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as an MPS within some tolerable error threshold. In previous work, we found that when solving the Vlasov-Poisson equations in 1D1V, important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Here, we investigate the practicality of using MPS methods for simulating (nonlinear) Landau damping in up to 3D3V and the speed-up the algorithm is able to provide.