  Quantum autoencoder is an efficient variational quantum algorithm for quantum
data compression. However, previous quantum autoencoders fail to compress and
recover high-rank mixed states. In this work, we discuss the fundamental
properties and limitations of the standard quantum autoencoder model in more
depth, and provide an information-theoretic solution to its recovering
fidelity. Based on this understanding, we present a noise-assisted quantum
autoencoder algorithm to go beyond the limitations, our model can achieve high
recovering fidelity for general input states. Appropriate noise channels are
used to make the input mixedness and output mixedness consistent, the noise
setup is determined by measurement results of the trash system. Compared with
the original quantum autoencoder model, the measurement information is fully
used in our algorithm. In addition to the circuit model, we design a
(noise-assisted) adiabatic model of quantum autoencoder that can be implemented
on quantum annealers. We verified the validity of our methods through
compressing the thermal states of transverse field Ising model and Werner
states. For pure state ensemble compression, we also introduce a projected
quantum autoencoder algorithm.
