Explore tensor network contraction optimization techniques in this 33-minute conference talk from the Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 workshop. Delve into hyper-optimized methods based on hypergraph partitioning for building efficient contraction trees. Discover a set of powerful tensor network simplifications designed to facilitate easier contraction. Examine applications in quantum circuit simulation and weighted model counting. Gain insights into extending these concepts to approximate contraction. Learn from Johnnie Gray of the California Institute of Technology as he presents advanced strategies for tackling complex tensor network geometries and improving computational efficiency.