Tropical Tensor Networks

Explore a unified exact tensor network approach for solving spin glass problems in this 25-minute conference talk by Lei Wang from the Chinese Academy of Sciences. Delve into the innovative use of Tropical Algebra in tensor networks to compute ground state energy, identify optimal configurations, and count solution numbers for spin glasses. Learn how this method combines concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, while leveraging GPU computational power. Discover applications in frustrated Ising models, combinatorial optimization, and square lattice spin glasses. Gain insights into the physical understanding of tropical algebra, gradient-based optimization, and the mixing of tropical and ordinary algebra for degeneracy counting.

Intro
Example: frustrated Ising model on a fog
Tropical tensor networks for Ising spin glasses
Tropical tensor network contraction → ground state energy value problemi
Physical understanding of the tropical algebra
Gradient with respect to the field → ground state configuration optimization proble
Mix tropical with ordinary algebra → ground state degeneracy counting problem
Counting with tensor networ
Exact computation on 1 Nvidia V100
More combinatorial optimization counting problems
Tensor network contraction orde
Solve spin glass with a quantum circuit simulator
Square lattice spin glasses
Chimera graph Ising spin glas
Summary