  Hidden Markov Models are widely used in classical computer science to model
stochastic processes with a wide range of applications. This paper concerns the
quantum analogues of these machines --- so-called Hidden Quantum Markov Models
(HQMMs). Using the properties of Quantum Physics, HQMMs are able to generate
more complex random output sequences than their classical counterparts, even
when using the same number of internal states. They are therefore expected to
find applications as quantum simulators of stochastic processes. Here, we
emphasise that open quantum systems with instantaneous feedback are examples of
HQMMs, thereby identifying a novel application of quantum feedback control.
