Efficient hierarchical Liouville space propagator to quantum dissipative dynamics.

We propose an efficient method to propagate the hierarchical quantum master equations based on a reformulation of the original formalism and the incorporation of a filtering algorithm that automatically truncates the hierarchy with a preselected tolerance. The new method is applied to calculate electron transfer dynamics in a spin-boson model and the absorption spectra of an excitonic dimmer. The proposed method significantly reduces the number of auxiliary density operators used in the hierarchical equation approach and thus provides an efficient way capable of studying real time dynamics of non-Markovian quantum dissipative systems in strong system-bath coupling and low temperature regimes.