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Tensor network compressed sensing with unsupervised machine learning
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DOI：10.1103/PhysRevResearch.2.033293.png)
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摘要
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We propose the tensor-network compressed sensing (TNCS) by incorporating the ideas of compressed sensing, tensor network (TN), and machine learning. The primary idea is to compress and communicate the real-life information through the generative TN state and by making projective measurements in a designed way. First, the state vertical bar Psi > is obtained by the unsupervised learning of TN, and then the data to be communicated are encoded in the separable state with the minimal distance to the projected state vertical bar Phi >, where vertical bar Phi > can be acquired by partially projecting vertical bar Psi >. A protocol analogous to the compressed sensing assisted by neural-network machine learning is thus suggested, where the projections are designed to rapidly minimize the uncertainty of information in vertical bar Phi >. To characterize the efficiency of TNCS, we propose a quantity named as q sparsity to describe the sparsity of quantum states, which is analogous to the sparsity of the signals required in the standard compressed sensing. The need of the q sparsity in TNCS is essentially due to the fact that the TN states obey the area law of entanglement entropy. The tests on the real-life data (handwritten digits and fashion images) show that the TNCS has competitive efficiency and accuracy.
Keyword:
SCHRODINGER CAT STATES
MATRIX PRODUCT STATES
QUANTUM
GENERATION
OPERATORS
PARTICLE
SPIN
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Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems量子自旋系统的矩阵乘积态，投影纠缠态和变分重归一化组方法.png)
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