  Exact and nonperturbative quantum master equation can be constructed via the
calculus on path integral. It results in hierarchical equations of motion for
the reduced density operator. Involved are also a set of well--defined
auxiliary density operators that resolve not just system--bath coupling
strength but also memory. In this work, we scale these auxiliary operators
individually to achieve a uniform error tolerance, as set by the reduced
density operator. An efficient propagator is then proposed to the hierarchical
Liouville--space dynamics of quantum dissipation. Numerically exact studies are
carried out on the dephasing effect on population transfer in the simple
stimulated Raman adiabatic passage scheme. We also make assessments on several
perturbative theories for their applicabilities in the present system of study.
