  For the efficient simulation of open quantum systems we often use quantum
jump trajectories given by pure states that evolve stochastically to unravel
the dynamics of the underlying master equation. In the Markovian regime, when
the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)
master equation, this procedure is known as Monte-Carlo wavefunction (MCWF)
approach . However, beyond ultraweak system-bath coupling, the dynamics of the
system is not described by an equation of GKSL type, but rather by the Redfield
equation, which can be brought into pseudo-Lindblad form. Here negative
dissipation strengths prohibit the conventional approach. To overcome this
problem, we propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling. It
does not require an effective extension of the state space, like other
approaches, except for the addition of a single classical bit. We test the PLQT
for the eternal non-Markovian master equation for a single qubit and an
interacting Fermi Hubbard chain coupled to a thermal bath and discuss its
computational effort compared to solving the full master equation.
