Exploring Hidden Quantum Markov Models

Does quantum information offer advantage in the prediction and simulation of classical stochastic processes? In this work I explore many examples of hidden quantum Markov models (HQMM), which are a quantum generalization of classical Markov chains. In particular, I discuss how a particular subset of HQMMs can be easily parametrized and generated. By studying their properties we can observe some non-intuitive features displayed by the improvement in memory requirements when going from classical to quantum models.