Research On Quantum Probabilistic Graphical Models

Abstract: The probabilistic graphical model is the product of probability theory and graphtheory and it provides the important way for solving the uncertain problems. Some learningalgorithms of the probabilistic graphical model will provide new method for the deeply research ofthe quantum information. In the field of quantum information, the problem of quantum statereconstruction has become a new research focus, the quantum states of the models can be estimatedby the parameter learning of the probabilistic graphical model. This article conbined theprobabilistic graphical models and quantum information and made the use of probabilistic to modelthe complex quantum systems, and quantum systems are researched by the use of probabilisticgraphical medel parameter estimation, probabilistic resoning theory of quantum systems. The maincontents are as follows:Firstly, the research method of classical probability graphical model was expanded and appliedto the quantum probabilitistic graphical models. A kind of quantum probabilistic graphical modelcomposed of quantum states, quantum operator and measurement was proposed subsequently.Furthermore, the structure of Quantum Hidden Markov Models and Quantum Markov RandomField Models as well as the parameter learning and probabilistic reasoning were studied in detail.Secondly, a discussion of the principles of classical EM algorithm and application of occasionswas made, and theoretically proved that the algorithm applied to the parameter estimation ofquantum probabilistic probabilistic graphical model was feasibility and had its advantages. It usedthe EM algorithm to learn the hidden quantum state in Quantum Hidden Markov Model from theperspective of the simulation to verify the effectiveness of the algorithm. The simulation resultsshowed that the mixing coefficient estimation error of quantum state decreased with the increasednumber of iterations; with the increasing number of samples, convergence speed of the algorithmbecame faster; meanwhile, the estimation error that characterized density matrix of quantum statedecreased with the increased number of steps of the model and finally, convergence, at the sametime, the algorithm has a rapid convergent speed. It illustrated that making the use of the EMalgorithm to study the problem of quantum probability graphical models had a certain advantages.Finally, a quantum markov random field model which has hierarchical structure was preliminarystudying. Starting from the structure of the model, the structural characteristics of quantum markovrandom field was analyzed. Lastly, the recursive relation between the quantum states which lie in the different layers of the quantum markov random field was derived theoretically, also someexamples was given to validate it.