  Hidden Quantum Markov Models (HQMMs) can be thought of as quantum
probabilistic graphical models that can model sequential data. We extend
previous work on HQMMs with three contributions: (1) we show how classical
hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we
reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum
circuits, and (3) we present a learning algorithm to estimate the parameters of
an HQMM from data. While our algorithm requires further optimization to handle
larger datasets, we are able to evaluate our algorithm using several synthetic
datasets. We show that on HQMM generated data, our algorithm learns HQMMs with
the same number of hidden states and predictive accuracy as the true HQMMs,
while HMMs learned with the Baum-Welch algorithm require more states to match
the predictive accuracy.
