Improved Convergence of Carleman-Embedded Quantum Algorithm for the Vlasov-Poisson System

Abstract

We extend the regime of convergence of Carleman-embedded quantum algorithms that solve the Vlasov-Poisson equations from kinetic plasma physics. We establish convergence, using both analytical and numerical lower bounds, for physically reasonable collision frequencies using a Fourier-Hermite expansion of the shifted phase-space distribution function. We also show that for a large class of basis functions, the convergence of the Carleman-embedded Vlasov-Poisson system requires increasing collision frequency strength with velocity resolution. The complexity of the quantum algorithm depends strongly on whether we seek time-averaged or -resolved outputs.