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Quantum Hidden Markov Models based on Transition Operation Matrices

Authors
  • Cholewa, Michał
  • Gawron, Piotr
  • Głomb, Przemysław
  • Kurzyk, Dariusz
Type
Preprint
Publication Date
Feb 16, 2016
Submission Date
Mar 30, 2015
Identifiers
arXiv ID: 1503.08760
Source
arXiv
License
Yellow
External links

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.

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