  We show that the general and numerically exact Hierarchy of Pure States
method (HOPS) is very well applicable to calculate the reduced dynamics of an
open quantum system. In particular we focus on environments with a sub-Ohmic
spectral density (SD) resulting in an algebraic decay of the bath correlation
function (BCF). The universal applicability of HOPS, reaching from weak to
strong coupling for zero and non-zero temperature, is demonstrated by solving
the spin-boson model for which we find perfect agreement with other methods,
each one suitable for a special regime of parameters. The challenges arising in
the strong coupling regime are not only reflected in the computational effort
needed for the HOPS method to converge but also in the necessity for an
importance sampling mechanism, accounted for by the non-linear variant of HOPS.
In order to include non-zero temperature effects in the strong coupling regime
we found that it is highly favorable for the HOPS method to use the zero
temperature BCF and include temperature via a stochastic Hermitian contribution
to the system Hamiltonian.
