A quantum algorithm for the linear Vlasov equation with collisions
Abstract
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this work, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional, electrostatic limit. Rather than solving this equation in its native spatial and velocity phase-space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. The Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. This representation results in a system of linear ordinary differential equations which can be solved with well-developed quantum algorithms: Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.
Cite
@article{arxiv.2303.03450,
title = {A quantum algorithm for the linear Vlasov equation with collisions},
author = {Abtin Ameri and Paola Cappellaro and Hari Krovi and Nuno F. Loureiro and Erika Ye},
journal= {arXiv preprint arXiv:2303.03450},
year = {2023}
}