Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning

We propose tensor-network compressed sensing (TNCS) for compressing and communicating classical information via the quantum states trained by the unsupervised tensor network (TN) machine learning. The main task of TNCS is to reconstruct as accurately as possible the full classical information from a generative TN state, by knowing as small part of the classical information as possible. In the applications to the datasets of hand-written digits and fashion images, we train the generative TN (matrix product state) by the training set, and show that the images in the testing set can be reconstructed from a small number of pixels. Related issues including the applications of TNCS to quantum encrypted communication are discussed.