On learning finite-state quantum sources

We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the {\em quantum generator} model to find that the analogous state of affairs holds: information-theoretically, a polynomial number of samples suffice to approximately identify the distribution, but computationally, the problem is as hard as learning parities with noise, a notorious open question in computational learning theory.