  Approaching the long-time dynamics of non-Markovian open quantum systems
presents a challenging task if the bath is strongly coupled. Recent proposals
address this problem through a representation of the so-called process tensor
in terms of a tensor network. We show that for Gaussian environments highly
efficient contraction to matrix product operator (MPO) form can be achieved
with infinite MPO evolution methods, leading to significant computational
speed-up over existing proposals. The result structurally resembles open system
evolution with carefully designed auxiliary degrees of freedom, as in
hierarchical or pseudomode methods. Here, however, these degrees of freedom are
generated automatically by the MPO evolution algorithm. Moreover, the
semi-group form of the resulting propagator enables us to explore steady-state
physics, such as phase transitions.
