  In this work, we extend the idea of Quantum Markov chains [S. Gudder. Quantum
Markov chains. J. Math. Phys., 49(7), 2008] in order to propose Quantum Hidden
Markov Models (QHMMs). For that, we use the notions of Transition Operation
Matrices (TOM) and Vector States, which are an extension of classical
stochastic matrices and probability distributions. Our main result is the Mealy
QHMM formulation and proofs of algorithms needed for application of this model:
Forward for general case and Vitterbi for a restricted class of QHMMs.
