Tensor Networks for Interpretable and Efficient Quantum-Inspired Machine Learning

It is a critical challenge to simultaneously achieve high interpretability and high efficiency with the current schemes of deep machine learning (ML). The tensor network (TN), a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages in developing efficient "white-box" ML schemes. Here, we provide a brief review of the inspiring progress in TN-based ML. On the one hand, the interpretability of TN ML can be accommodated by a solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be obtained from powerful TN representations and the advanced computational techniques developed in quantum many-body physics. Keeping pace with the rapid development of quantum computers, TNs are expected to produce novel schemes runnable on quantum hardware in the direction of "quantum artificial intelligence" in the near future.