On compression rate of quantum autoencoders: Control design, numerical and experimental realization. (January 2023)

• Record Type: Journal Article
• Authors: Ma, Hailan; Huang, Chang-Jiang; Chen, Chunlin; Dong, Daoyi; Wang, Yuanlong; Wu, Re-Bing; Xiang, Guo-Yong
• Is Part Of: Automatica. Volume 147(2023)
• Publication Date: 2023-01
• Subjects: Quantum autoencoder -- Quantum control -- Learning control -- Compression rate; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110659
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the compression rate for a given quantum autoencoder and present a learning control approach for training the autoencoder to achieve the maximal compression rate. The upper bound of the compression rate is theoretically proven using eigen-decomposition and matrix differentiation, which is determined by the eigenvalues of the density matrix representation of the input states. Numerical results on 2-qubit and 3-qubit systems are presented to demonstrate how to train the quantum autoencoder to achieve the theoretically maximal compression, and the training performance using different machine learning algorithms is compared. Experimental results of a quantum autoencoder using quantum optical systems are illustrated for compressing two 2-qubit states into two 1-qubit states.