  A sequence of controlled collisions between a quantum system and its
environment (composed of a set of quantum objects) naturally simulates (with
arbitrary precision) any Markovian quantum dynamics of the system under
consideration. In this paper we propose and study the problem of simulation of
an {\it arbitrary} quantum channel via collision models. We show that a
correlated environment is capable to simulate {\it non-Markovian} evolutions
leading to any indivisible qubit channel. In particular, we derive the
corresponding master equation generating a continuous time non-Markovian
dynamics implementing the universal NOT gate being an example of the most
non-Markovian quantum channels.
