Loop series expansions for tensor networks

作者：Glen Evenbly, Nicola Pancotti, Ashley Milsted, Johnnie Gray, Garnet Kin‐Lic Chan · 发表于：Physical Review Research · 年份：2026 · DOI：10.1103/vqks-cr6x · 被引用次数：5 · 研究领域：Computational Physics and Python Applications、Model Reduction and Neural Networks、Modeling and Simulation Systems

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this article, we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of infinite projected entangled pair states, either representing the ground state of an Affleck-Kennedy-Lieb-Tasaki (AKLT) model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude while incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines.