Quantum Algorithms for Plasma Physics Simulations*

The nonlinearity of plasma physics makes its numerical simulations resource-expensive. It is natural to seek alternative computational platforms that may offer speedups of such simulations. Quantum computers are an attractive option, as they have the potential to solve certain problems exponentially or polynomially faster than classical computers (Grover 1996, Shor 1999). We investigate two approaches to simulating plasma physics on quantum computers. First, we consider the linearized Vlasov equation with collisions. Using a Fourier expansion in real space and Hermite expansion in velocity space, we obtain a system of differential equations (Kanekar et al. 2014) that can be solved using Hamiltonian simulation and operator splitting (i.e., Trotterization) techniques on a quantum computer (e.g., Childs and Wiebe 2012). The second approach considers discrete time quantum walks, which are analogous to classical random walks. In the continuous limit, such quantum walks can converge to Schrodinger's equation (Hatifi et al. 2019), which can be mapped to the MHD equations using the Madelung transform (Dodin and Startsev 2020). Thus, by implementing these quantum walks on a quantum computer, we can simulate certain classes of MHD problems.