Quantum autoencoders using mixed reference states

TL;DR

This paper introduces a novel quantum autoencoder approach that uses mixed reference states to improve data compression fidelity, overcoming entropy limitations of pure reference states, demonstrated through simulations and IBM quantum experiments.

Contribution

It proposes a new cost function incorporating quantum mutual information and explores mixed reference states, enhancing quantum autoencoder performance beyond previous pure state methods.

Findings

Improved encoding fidelity with mixed reference states

Effective strategies for setting mixedness ratios

Successful experimental validation on IBM quantum devices

Abstract

One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a reference state. When taking a pure reference state, there exists an upper bound for the encoding fidelity, which limits the compression of states with high entropy. To overcome the entropy inconsistency, we allow the reference state to be a mixed state and propose a cost function that combines the encoding fidelity and the quantum mutual information. We consider the reference states to be a mixture of maximally mixed states and pure states and propose three strategies for setting the ratio of mixedness. Numerical simulations of different states and experimental implementations on IBM quantum devices illustrate the effectiveness of our approach.