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arXiv:1905.01331

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

Ashley Milsted, Martin Ganahl, Stefan Leichenauer, Jack D. Hidary, Guifré Vidal

Published May 3, 2019• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1905.01331

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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 χχχ, with a computational cost that scales as O(χ4)O(χ^4)O(χ4). Using bond dimension χ∈[32,256]χ\in [32,256]χ∈[32,256] we compare the use of CPUs with GPUs and observe significant computational speed-ups, up to a factor of 100100100, using a GPU and the TensorNetwork library.
We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a way that is parallelizable and well-suited to automatic gradients for optimization. Applying the technique to the MNIST and Fashion-MNIST datasets we find out-of-the-box performance of 98% and 88% accuracy, respectively, using the same tensor network architecture. The TensorNetwork library allows us to seamlessly move from CPU to GPU hardware, and we see a factor of more than 10 improvement in computational speed using a GPU.
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