Quantum sparse coding and decoding based on quantum network

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.