Matrix eigenvalue solver based on reconfigurable photonic neural network
Liao Kun,
Li Chentong,
Dai Tianxiang,
Zhong Chuyu,
Lin Hongtao,
Hu Xiaoyong,
Gong Qihuang
Affiliations
Liao Kun
State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing100871, China
Li Chentong
State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing100871, China
Dai Tianxiang
State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing100871, China
Zhong Chuyu
College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou310027, China
Lin Hongtao
College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou310027, China
Hu Xiaoyong
State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing100871, China
Gong Qihuang
State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing100871, China
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.
