Automatic Contraction of Unstructured Tensor Networks

Abstract

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

34 pages, 31 figures. Resubmission to SciPost

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Cited by in corpus (6)

• Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Algorithms for Tensor Network Contraction Ordering
• Avoidance, Adjacency, and Association in Distributed Systems Design
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm