AUTHOR=Zhang Tianning , Chen Tianqi , Li Erping , Yang Bo , Ang L. K. 

TITLE=Stack Operation of Tensor Networks

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.906399

DOI=10.3389/fphy.2022.906399

ISSN=2296-424X

ABSTRACT=The tensor network, as a factorization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network contraction is so far well defined. In this paper, we propose a mathematically rigorous definition for the tensor network stack approach, that compress a large amount of tensor networks into a single one without changing their structures and configurations. 
     We illustrate the main ideas with the matrix product states based machine learning as an example. Our results are compared with the for loop and the efficient coding method on both CPU and GPU.