  Extending classical probabilistic reasoning using the quantum mechanical view
of probability has been of recent interest, particularly in the development of
hidden quantum Markov models (HQMMs) to model stochastic processes. However,
there has been little progress in characterizing the expressiveness of such
models and learning them from data. We tackle these problems by showing that
HQMMs are a special subclass of the general class of observable operator models
(OOMs) that do not suffer from the \emph{negative probability problem} by
design. We also provide a feasible retraction-based learning algorithm for
HQMMs using constrained gradient descent on the Stiefel manifold of model
parameters. We demonstrate that this approach is faster and scales to larger
models than previous learning algorithms.
