  As a ubiquitous aspect of modern information technology, data compression has
a wide range of applications. Therefore, a quantum autoencoder which can
compress quantum information into a low-dimensional space is fundamentally
important to achieve automatic data compression in the field of quantum
information. Such a quantum autoencoder can be implemented through training the
parameters of a quantum device using classical optimization algorithms. In this
article, we analyze the condition of achieving a perfect quantum autoencoder
and theoretically prove that a quantum autoencoder can losslessly compress
high-dimensional quantum information into a low-dimensional space (also called
latent space) if the number of maximum linearly independent vectors from input
states is no more than the dimension of the latent space. Also, we
experimentally realize a universal two-qubit unitary gate and design a quantum
autoencoder device by applying machine learning method. Experimental results
demonstrate that our quantum autoencoder is able to compress two two-qubit
states into two one-qubit states. Besides compressing quantum information, the
quantum autoencoder is used to experimentally discriminate two groups of
nonorthogonal states.
