Accelerating tensor-network contraction by dimension reduction

Z. Y. Xie, H. J. Liao, Rui-Zhen Huang, Haidong Xie, Jianjun Chen, Z. Y. Liu, Tao Xiang

Published May 24, 2017• 0 citations

Abstract

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost for carrying out this contraction is generally very high, which limits the largest bond dimension of tensor-network states that can be accurately studied to a relatively small value. We propose a dimension reduction scheme to solve this problem by mapping the double-layer tensor network onto an intersected single-layer tensor network. This reduces greatly the bond dimensions of local tensors to be contracted, and improves dramatically the efficiency and accuracy in the evaluation of expectation values of tensor-network states. It almost doubles the largest bond dimension of tensor-network states whose physical properties can be efficiently and reliably calculated, and extends significantly the application scope of tensor-network methods.

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