I will have a brief introduction to the graph representation of a tensor network, and the efforts people made to find the optimal way to contract it. To be specific, I will introduce several concepts in graph theory elimination ordering and tree width by examples, as well as the gist of several algorithms to find the optimal tree width. Given time, I will show how to map a quantum circuit simulation into a tensor network contraction problem.

References:

1. Igor L. Markov and Yaoyun Shi, "Simulating quantum computation by contracting tensor networks", SIAM Journal on Computing 38.3 (2008): 963-981.