arXiv 1905.013312019-05-03cond-mat.str-elcs.LGhep-thphysics.comp-phstat.ML

TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networks

Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；Alphabet (Google) X（Alphabet（谷歌）X）

Ashley Milsted, Martin Ganahl, Stefan Leichenauer, Jack Hidary, Guifre Vidal

备注：: All code can be found at https://github.com/google/tensornetwork

英文摘要：

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice model on a thin torus (2D), and implement the algorithm using TensorNetwork. We use a standard energy minimization procedure over a TTN ansatz with bond dimension $χ$, with a computational cost that scales as $O(χ^4)$. Using bond dimension $χ\in [32,256]$ we compare the use of CPUs with GPUs and observe significant computational speed-ups, up to a factor of $100$, using a GPU and the TensorNetwork library.

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