Sparse coding provides a versatile framework for efficiently capturing and representing crucial data (information) concisely, which plays an essential role in various computer science fields, including data compression, feature extraction, and general signal processing. Here, we propose symmetric quantum neural networks for realizing sparse coding and decoding algorithms. Our networks consist of multi-layer, two-level unitary transformations that are naturally suited for optical circuits. Specifically, the two networks we propose can be efficiently trained together or separately via a quantum natural gradient descent algorithm. Utilizing the trained model, we achieve coding and decoding of sparse data including sparse classical data of binary and grayscale images, as well as sparse quantum data that are quantum states in a certain smaller subspace. The results demonstrate an accuracy of 98.77% for image reconstruction and a fidelity of 97.68% for quantum state revivification. Our quantum sparse coding and decoding model offers improved generalization and robustness compared to the classical model, giving insights to further research on quantum advantages in artificial neural networks.

中文翻译：

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基于量子网络的量子稀疏编解码


稀疏编码提供了一个多功能框架，可以有效地简洁地捕获和表示关键数据（信息），这在各种计算机科学领域中发挥着至关重要的作用，包括数据压缩、特征提取和一般信号处理。在这里，我们提出了用于实现稀疏编码和解码算法的对称量子神经网络。我们的网络由多层、两级的酉转换组成，这些转换自然适合于光电路。具体来说，我们提出的两个网络可以通过量子自然梯度下降算法一起或单独有效地训练。利用训练好的模型，我们实现了稀疏数据的编码和解码，包括二进制和灰度图像的稀疏经典数据，以及在某个较小的子空间中属于量子态的稀疏量子数据。结果表明，图像重建的准确率为 98.77%，量子态复兴的保真度为 97.68%。与经典模型相比，我们的量子稀疏编码和解码模型提供了改进的泛化性和鲁棒性，为进一步研究人工神经网络中的量子优势提供了见解。