Quantum Belief Propagation Algorithm versus Suzuki-Trotter approach in   the one-dimensional Heisenberg chains
  Quantum systems are the future candidates for computers and information processing devices. Information about quantum states and processes may be incomplete and scattered in these systems. We use a quantum version of Belief Propagation(BP) Algorithm to integrate the distributed information. In this algorithm the distributed information, which is in the form of density matrix, can be approximated to local structures. The validity of this algorithm is measured in comparison with Suzuki-Trotter(ST) method, using simulated information. ST in 3-body Heisenberg example gives a more accurate answer, however Quantum Belief Propagation (QBP) runs faster based on complexity. In order to develop it in the future, we should be looking for ways to increase the accuracy of QBP. 
Farzad Ghafari Jouneghani, Mohammad Babazadeh, Davoud Salami, Hossein   Movla
quant-ph cs.IT math.IT