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

3 May 2019  ·  Ashley Milsted, Martin Ganahl, Stefan Leichenauer, Jack Hidary, Guifre Vidal ·

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 $\chi$, with a computational cost that scales as $O(\chi^4)$. Using bond dimension $\chi \in [32,256]$ 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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