Matrix product state for quantum-inspired feature extraction and compressed sensing

Improving the interpretability and efficiency of machine learning methods are challenging and important issues. The concept of entanglement, which is a quantity from quantum information science, may contribute to these issues. In this extended abstract, we introduce two tensor-network (TN) machine learning methods, which concerns feature extraction and compressed sensing, respectively, based on entanglement. For the former [Front. Appl. Math. Stat. 7, 716044 (2021)], the entanglement obtained from matrix product state (MPS) is used as a measure of the importance of the features in the real-life datasets. An entanglement-based feature extraction algorithm is proposed, and used to improve the efficiency of TN machine learning. In the latter [Phys. Rev. Research. 2, 033293 (2020)], TN states are used to realize efficient compressed sampling by entanglement-guided projective measurements. This scheme can be applied in the future to compress and communicate the real-life data by entangled qubits.