Discretising the Herman-Kluk propagator

The Herman-Kluk propagator is a well-known semi-classical approximation of the unitary evolution operator in quantum molecular dynamics. In this paper we formulate the Herman-Kluk propagator as a phase space integral and discretise it by Monte Carlo and quasi-Monte Carlo quadrature. Then, we investigate the accuracy of a symplectic time discretisation by combining backward error analysis with Fourier integral operator calculus. Numerical experiments for two- and six-dimensional model systems support our theoretical results.