Stack operation of tensor networks
This work addresses a foundational issue in tensor network operations for researchers in quantum computing and machine learning, but it appears incremental as it defines a specific operation rather than introducing a new paradigm.
The paper tackles the problem of stacking tensor networks, which was previously undefined due to non-unique structures, by proposing a mathematically rigorous definition that compresses multiple tensor networks into one without altering their configurations. The results show comparisons with for loops and efficient coding methods on CPU and GPU, though no concrete numbers are provided.
The tensor network, as a facterization 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.