Hidden Markov Model Based On Open Quantum Walking

In the classical computational science,the Hidden Markov Models is widely used in speech recognition,biological sequence analysis and other fields.In 2011,A.Monras first proposed the concept of Hidden Quantum Markov Models,and the Hidden Quantum Markov Models can represent more complex observation sequences than the classical Hidden Markov Models.In recent years,the researchers have focused on the study of Hidden Markov Models in open quantum systems.In order to solve the basic problem of the Hidden Markov Models,this paper proposes to build a Hidden Markov Model with open quantum random walk in open quantum system.Firstly,the model will prepare the implicit state and the observed state of the quantum state.Then design the transfer operator and the observation operator.The evaluation problem is solved by directly obtaining the observation state sequence measurement results.Single-step measurement of observation state and the use of feedback information combined with the classic Viterbi algorithm applied to the decoding problem.The simulation results show that the results are the same for the same observation sequence,when we use the quantum algorithm and the classical algorithm to solve the problem,but the time complexity of the quantum algorithm is reduced to O(N).When the number of hidden states is large enough,the quantum algorithm and the classical algorithm to solve the problem of decoding have the same degree of more than 95%.In addition,by improving the accuracy of the measurement feedback information,the quantum algorithm can improve the decoding ability,so the quantum algorithm can be effective solve the decoding problem.