Optimized Quantum Autoencoder

TL;DR

This paper presents a method to optimize quantum autoencoders by minimizing the quantum mutual information between subsystems, leading to improved compression of mixed quantum states.

Contribution

It introduces a theoretical framework for reducing information loss in QAE and proposes a decomposition of the encoding unitary, enhancing the design process.

Findings

The lost information equals the quantum mutual information between subsystems.

Optimized unitaries can be decomposed into permutation and disentanglement transformations.

Our scheme outperforms existing variational circuit-based QAEs.

Abstract

Quantum autoencoder (QAE) compresses a bipartite quantum state into its subsystem by a self-checking mechanism. How to characterize the lost information in this process is essential to understand the compression mechanism of QAE\@. Here we investigate how to decrease the lost information in QAE for any input mixed state. We theoretically show that the lost information is the quantum mutual information between the remaining subsystem and the ignorant one, and the encoding unitary transformation is designed to minimize this mutual information. Further more, we show that the optimized unitary transformation can be decomposed as the product of a permutation unitary transformation and a disentanglement unitary transformation, and the permutation unitary transformation can be searched by a regular Young tableau algorithm. Finally we numerically identify that our compression scheme outperforms the quantum variational circuit based QAE\@.