A Quantum Algorithm for the Collisional Linearized Vlasov Equation

Simulating plasma dynamics is notoriously challenging. It is natural to seek alternative computational platforms that may speed up such simulations. Quantum computers are an attractive option, as they can solve certain problems exponentially or polynomially faster than classical computers (Grover 1996, Shor 1999). This project aims to investigate whether quantum algorithms can speed up plasma simulations. As a first step, we consider a quintessential plasma problem: Landau damping. Using a Fourier expansion in real space and a Hermite expansion in velocity space, we obtain, from the linearized Vlasov equation, a system of differential equations (Kanekar et al. 2014) which can be mapped to Schrodinger’s equation. In the collisionless limit, we attain unitary time evolution from a Hermitian Hamiltonian, which can be implemented on a quantum computer using Hamiltonian simulation techniques (e.g., Berry et al. 2015). Our algorithm is more flexible than previous ones (Engel et al. 2019) in that it allows for different target problems and it can be naturally extended to the collisional case. In this more realistic scenario, while unitarity is lost, Trotterization can be used to simulate the system by splitting the classical Hamiltonian into a Hermitian and a non-Hermitian matrix.