Tensor networks for interpretable and efficient quantum-inspired machine learning

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages on developing efficient white-box'' ML schemes. Here, we give a brief review on the inspiring progresses made in TN-based ML. On one hand, interpretability of TN ML is accommodated with the solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be rendered from the powerful TN representations and the advanced computational techniques developed in quantum many-body physics. With the fast development on quantum computers, TN is expected to conceive novel schemes runnable on quantum hardware, heading towards the quantum artificial intelligence’’ in the forthcoming future.