Investigation of commuting Hamiltonian in quantum Markov network
This provides a foundational extension of graphical models to quantum domains, potentially benefiting quantum information and statistical physics.
The paper generalized classical Markov networks to quantum systems and investigated how commuting Hamiltonian terms affect conditional independence in quantum statistical physics, using simple examples to demonstrate the relationship.
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 been 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 preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics.We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.