标题： 张量网络的环路级数展开 显示英文标题

标题： Loop Series Expansions for Tensor Networks

摘要： 信念传播（BP）可以作为一种有用的工具，近似地收缩张量网络，前提是网络中任何闭合环路的贡献足够弱。 在本文中，我们描述了如何应用环系列展开来系统地提高BP对张量网络收缩的近似精度，在理论上可以收敛到精确结果的任意接近程度。 更一般地，我们的结果提供了一个框架，将张量网络展开为一个层次结构中复杂度逐渐增加的组件网络之和。 我们对iPEPS的收缩进行了基准测试，无论是代表AKLT模型的基态还是具有随机定义张量的情况，结果表明其准确性比标准BP提高了几个数量级，而计算成本仅略有增加。 这些结果表明，所提出的系列展开可能是在现有收缩方法无法处理的情况下准确评估张量网络的有用工具。 显示英文摘要

摘要： 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 manuscript 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 iPEPS, either representing the ground state of an AKLT model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude whilst 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.