Improved Convergence of Carleman-Embedded Quantum Algorithm for the Vlasov-Poisson System
arXiv:2607.28426
The paper improves the convergence analysis of a Carleman-embedded quantum algorithm for solving the Vlasov‑Poisson equations, providing analytical and numerical bounds and examining how collision frequency and velocity resolution affect algorithm complexity.
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.
11 pages, 2 figures