  Techniques for approximately contracting tensor networks are limited in how
efficiently they can make use of parallel computing resources. In this work we
demonstrate and characterize a Monte Carlo approach to the tensor network
renormalization group method which can be used straightforwardly on modern
computing architectures. We demonstrate the efficiency of the technique and
show that Monte Carlo tensor network renormalization provides an attractive
path to improving the accuracy of a wide class of challenging computations
while also providing useful estimates of uncertainty and a statistical
guarantee of unbiased results.
