A review of Quantum Graphical Models

Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is prepare a primary generalization of graphical models to quantum case and applying in quantum statistical physics in order to simulating of many body systems and inferring quantum states. We have investigated the graphical models and the role of commutativity or non-commutativity of hamiltonian terms in conditional independence with simple examples of quantum statistical physics.