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 which consist of a set of independent degrees of freedom. 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, anharmonic environments, dispersive coupling to time-dependent lossy cavity modes, and superradiance. The versatility and efficiency of our automated compression of environments (ACE) method provides a practical general-purpose tool for open quantum systems.
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