Matrix eigenvalue solver based on reconfigurable photonic neural network

Area of Science:

• Numerical analysis
• Photonic computing
• Artificial intelligence

Background:

• Eigenvalue problem is crucial in engineering and science.
• Existing algorithms lack photonic implementation.
• Photonic neural networks offer speed and low energy consumption.

Purpose of the Study:

• Propose a photonic neural network for real-value symmetric matrix eigenvalue solving.
• Demonstrate feasibility on a photonic platform.
• Enable on-chip integrated all-optical computing.

Main Methods:

• Utilized reconfigurable photonic neural networks.
• Employed graphene/Si thermo-optical modulation.
• Incorporated a saturated absorption nonlinear activation layer.
• Tested on 2x2, 3x3, and 4x4 matrices.

Main Results:

• Demonstrated eigenvalue solving for real-value symmetric matrices.
• Achieved 78.8% experimental accuracy for 4x4 matrices.
• Theoretically predicted 93.6% accuracy for 2x2 matrices.

Conclusions:

• The proposed strategy is feasible for on-chip photonic eigenvalue solvers.
• This work lays the foundation for next-generation all-optical computing.
• Enables efficient and high-speed matrix computations.