Tensor Network Approaches for Quantum Many-body Physics and Machine Learning

Tensor network (TN) has been recognized as a powerful numerical tool applied in various fields in physics, computer sciences, etc. TN originates from quantum physics as an efficient representation of quantum many-body states and their operations. It serves as one of the most important approaches for simulating interacting spins, bosons, and fermions, at zero and finite temperatures. It has no “negative sign” problems, thus provides a promising way to handle the systems with geometrical frustration and the fermionic models away from half-filling. TN is also closely related to the models in quantum information and computation, such as quantum circuits. Significant progress has been achieved with TN in the hybridization of quantum information sciences and condensed matter physics, such as symmetry-protected topological quantum computation. Recently, TN shows great perspective as a quantum-inspired model for machine learning interpreted by quantum theories and runnable on quantum computers.

The main goal of this Research Topic is to provide a platform to report on the recent progress and results in tensor network algorithms and their applications in simulating the strongly-correlated quantum systems and machine learning. We welcome both research and review articles and highly encourage those that have interest in the interdisciplinary fields to shed light on the hybridizations of quantum physics and computer sciences.

This Research Topic would be focused on the following problems:
(1) Efficient algorithms for tensor network contractions and applications to quantum lattice models;
(2) Tensor network for quantum information and computation;
(3) Tensor network for quantum-inspired machine learning and quantum intelligence;
(4) Hybridizations among tensor decompositions, neural networks, and tensor networks for machine learning.