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arXiv · 2303.03450

A quantum algorithm for the linear Vlasov equation with collisions

Abtin Ameri·Paola Cappellaro·Hari Krovi·Nuno F. Loureiro·Erika Ye
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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.

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Abtin Ameri, Paola Cappellaro, Hari Krovi, Nuno F. Loureiro, Erika Ye. 2023-03-06. A quantum algorithm for the linear Vlasov equation with collisions. https://doi.org/10.1103/physreva.107.062412

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