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 verify the validity of our methods through compressing the thermal states of the transverse-field Ising model and Werner states. For pure-state ensemble compression, we also introduce a projected quantum-autoencoder algorithm.

中文翻译：

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噪声辅助量子自编码器

量子自动编码器是一种用于量子数据压缩的高效变分量子算法。但是，以前的量子自动编码器无法压缩和恢复高级混合状态。在这项工作中，我们将更深入地讨论标准量子自动编码器模型的基本属性和局限性，并为其恢复保真度提供信息理论的解决方案。基于这种理解，我们提出了一种噪声辅助的量子自动编码器算法，以超越限制，我们的模型可以为一般输入状态实现高恢复保真度。适当的噪声通道用于使输入混合度和输出混合度一致，噪声设置取决于垃圾系统的测量结果。与原始的量子自动编码器模型相比，测量信息已在我们的算法中得到了充分利用。除了电路模型外，我们还设计了一种量子自动编码器（噪声辅助）绝热模型，该模型可以在量子退火器上实现。我们通过压缩横向场伊辛模型的热态和Werner态验证了我们方法的有效性。对于纯状态集成压缩，我们还介绍了一种投影量子自动编码器算法。