Shortcut Matrix Product States and its applications

Understand

Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various applications such as compressing high-dimensional data, supervised kernel linear classifier, and unsupervised generative modeling.

• However, when applied to systems which are not defined on one-dimensional lattices, a serious drawback of the MPS is the exponential decay of the correlations, which limits its power in capturing long-range dependences among variables in the system.
• To alleviate this problem, we propose to introduce long-range interactions, which act as shortcuts, to MPS, resulting in a new model \textit{ Shortcut Matrix Product States} (SMPS).
• When chosen properly, the shortcuts can decrease significantly the correlation length of the MPS, while preserving the computational efficiency.