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- W4380321969 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 paper, 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. For a given simulation time, 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 (ODEs) which can be solved with well-developed quantum algorithms: a 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." @default.
- W4380321969 created "2023-06-13" @default.
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- W4380321969 date "2023-06-12" @default.
- W4380321969 modified "2023-09-27" @default.
- W4380321969 title "Quantum algorithm for the linear Vlasov equation with collisions" @default.
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- W4380321969 doi "https://doi.org/10.1103/physreva.107.062412" @default.
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