  The central challenge for describing the dynamics in open quantum systems is
that the Hilbert space of typical environments is too large to be treated
exactly. In some cases, such as when the environment has a short memory time or
only interacts weakly with the system, approximate descriptions of the system
are possible. Beyond these, numerically exact methods exist, but these are
typically restricted to baths with Gaussian correlations, such as
non-interacting bosons. Here we present a numerically-exact method for
simulating open quantum systems with arbitrary environments. Our approach
automatically reduces the large number of environmental degrees of freedom to
those which are most relevant. Specifically, we show how the process tensor --
which describes the effect of the environment -- can be iteratively constructed
and compressed using matrix product state techniques. We demonstrate the power
of this method by applying it to problems with bosonic, fermionic, and spin
environments: electron transport, phonon effects and radiative decay in quantum
dots, central spin dynamics, and superradiance. The versatility and efficiency
of our automated compression of environments (ACE) method provides a practical
general-purpose tool for open quantum systems.
