  In this paper we develop a novel method to solve problems involving quantum
optical systems coupled to coherent quantum feedback loops featuring time
delays. Our method is based on exact mappings of such non-Markovian problems to
equivalent Markovian driven dissipative quantum many-body problems. In this
work we show that the resulting Markovian quantum many-body problems can be
solved (numerically) exactly and efficiently using tensor network methods for a
series of paradigmatic examples, consisting of driven quantum systems coupled
to waveguides at several distant points. In particular, we show that our method
allows solving problems in so far inaccessible regimes, including problems with
arbitrary long time delays and arbitrary numbers of excitations in the delay
lines. We obtain solutions for the full real-time dynamics as well as the
steady state in all these regimes. Finally, motivated by our results, we
develop a novel mean-field approach, which allows us to find the solution
semi-analytically and identify parameter regimes where this approximation is in
excellent agreement with our exact tensor network results.
