Hyper-optimized approximate contraction of tensor networks with arbitrary geometry

• URL: http://arxiv.org/abs/2206.07044v2
• Date: Thu, 5 Oct 2023 23:00:42 GMT
• Title: Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Authors: Johnnie Gray and Garnet Kin-Lic Chan
• Abstract summary: We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyper-optimization over the compression and contraction strategy itself to minimize error and cost.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyper-optimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both hand-crafted contraction strategies in the literature as well as recently proposed general contraction algorithms on a variety of synthetic and physical problems on regular lattices and random regular graphs. We further showcase the power of the approach by demonstrating approximate contraction of tensor networks for frustrated three-dimensional lattice partition functions, dimer counting on random regular graphs, and to access the hardness transition of random tensor network models, in graphs with many thousands of tensors.

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