## Tropical Tensor Networks

#### Lei WangChinese Academy of Sciences

I will present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra defined on the semiring. Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the usual algebra counts the ground state degeneracy. The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes computational power of graphical processing units.

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