The solution of matrix eigenvalues has always been a research hotspot in the field of modern numerical analysis, which has important value in practical application of engineering technology and scientific research. Despite the fact that currently existing algorithms for solving the eigenvalues of matrices are well-developed to try to satisfy both in terms of computational accuracy and efficiency, few of them have been able to be realized on photonic platform. The photonic neural network not only has strong judgment in solving inference tasks due to the superior learning ability, but also makes full use of the advantages of photonic computing with ultrahigh speed and ultralow energy consumption. Here, we propose a strategy of an eigenvalue solver for real-value symmetric matrices based on reconfigurable photonic neural networks. The strategy shows the feasibility of solving the eigenvalues of real-value symmetric matrices of n × n matrices with locally connected networks. Experimentally, we demonstrate the task of solving the eigenvalues of 2 × 2, 3 × 3, and 4 × 4 real-value symmetric matrices based on graphene/Si thermo-optical modulated reconfigurable photonic neural networks with saturated absorption nonlinear activation layer. The theoretically predicted test set accuracy of the 2 × 2 matrices is 93.6% with the measured accuracy of 78.8% in the experiment by the standard defined for simplicity of comparison. This work not only provides a feasible solution for the on-chip integrated photonic realization of eigenvalue solving of real-value symmetric matrices, but also lays the foundation for a new generation of intelligent on-chip integrated all-optical computing.

Photonic neural networks benefit from the use of photons to perform intelligent inference computing with ultrafast and ultralow energy consumption in ultra-high-throughput, providing the efficient photonic hardware for the new generation of intelligent computing, and the effective way to support large-scale integration for on-chip all-optical computing chips. With the rapid development of photonic neural networks, demands for efficient computation power have increased dramatically. However, the weak and impractical optical nonlinear activations, the lack of suitable configurations for integrated photonic hardware, and proper optical storage mediums pose challenges to this field. In this Perspective, we propose our current point of view and a suggestive roadmap in the field of integrated photonic platform for optical neural networks. Throughout the discussion, we highlight recent progresses meeting with major challenges. We also identify some next challenges still ahead to realize integrated photonic neural networks capable of matching the current computational power of graphic cards.