  We present a general scheme to map correlated nonequilibrium quantum impurity
problems onto an auxiliary open quantum system of small size. The infinite
fermionic reservoirs of the original system are thereby replaced by a small
number $N_B$ of noninteracting auxiliary bath sites whose dynamics is described
by a Lindblad equation. Due to the presence of the intermediate bath sites, the
overall dynamics acting on the impurity site is non-Markovian.
  With the help of an optimization scheme for the auxiliary Lindblad
parameters, an accurate mapping is achieved, which becomes exponentially exact
upon increasing $N_B$. The basic idea for this scheme was presented previously
in the context of nonequilibrium dynamical mean field theory. In successive
works on improved manybody solution strategies for the auxiliary Lindblad
equation, such as Lanczos exact diagonalization or matrix product states, we
applied the approach to study the nonequilibrium Kondo regime.
  In the present paper, we address in detail the mapping procedure itself,
rather than the many-body solution. In particular, we investigate the effects
of the geometry of the auxiliary system on the accuracy of the mapping for
given $N_B$. Specifically, we present a detailed convergence study for five
different geometries which, besides being of practical utility, reveals
important insights into the underlying mechanisms of the mapping. For setups
with onsite or nearest-neighbor Lindblad parameters we find that a
representation adopting two separate bath chains is by far more accurate with
respect to other choices based on a single chain or a commonly used star
geometry. A significant improvement is obtained by allowing for long-ranged and
complex Lindblad parameters. These results can be of great value when studying
Lindblad-type approaches to correlated systems.
