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We present a general method for approximately contracting tensor networkswith an arbitrary connectivity. This enables us to release the computationalpower of tensor networks to wide use in inference and learning problems definedon general graphs. We show applications of our algorithm in graphical models,specifically on estimating free energy of spin glasses defined on various ofgraphs, where our method largely outperforms existing algorithms including themean-field methods and the recently proposed neural-network-based methods. Wefurther apply our method to the simulation of random quantum circuits, anddemonstrate that, with a trade off of negligible truncation errors, our methodis able to simulate large quantum circuits that are out of reach of thestate-of-the-art simulation methods.

Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations