  Tensor networks are the main building blocks in a wide variety of
computational sciences, ranging from many-body theory and quantum computing to
probability and machine learning. Here we propose a parallel algorithm for the
contraction of tensor networks using probabilistic graphical models. Our
approach is based on the heuristic solution of the $\mu$-treewidth deletion
problem in graph theory. We apply the resulting algorithm to the simulation of
random quantum circuits and discuss the extensions for general tensor network
contractions.
