论文标题
用任意几何形状的张量网络超优化的近似近似收缩
Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
论文作者
论文摘要
张量网络收缩是从多体物理学到计算机科学的问题。我们描述了如何通过在任意图上的键压缩来近似张量的网络收缩。特别是，我们在压缩和收缩策略本身中引入了一个高度优化，以最大程度地减少错误和成本。我们证明，我们的协议在文献中优于手工制作的收缩策略，以及最近在常规晶格和随机常规图的各种合成和物理问题上提出的一般收缩算法。我们通过证明张紧网络的近似收缩来展示该方法的功能，以挫败三维晶格分区功能，在随机常规图上计数二聚体，并访问与数千张量子的图形。
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.
