Quantum Hidden Markov Models based on Transition Operation Matrices

TL;DR

This paper introduces Quantum Hidden Markov Models (QHMMs) built on Transition Operation Matrices, extending quantum Markov chains, with algorithms for inference like Forward and Viterbi tailored for these models.

Contribution

It proposes a novel formulation of QHMMs using TOMs and vector states, along with algorithms for their practical application.

Findings

Formulated Mealy QHMMs and proved their properties.

Developed Forward and Viterbi algorithms for QHMMs.

Extended classical stochastic concepts to quantum models.

Abstract

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.