A small microring array that performs large complex-valued matrix-vector multiplication

As an important computing operation, photonic matrix-vector multiplication is widely used in photonic neutral networks and signal processing. However, conventional incoherent matrix-vector multiplication focuses on real-valued operations, which cannot work well in complex-valued neural networks and discrete Fourier transform. In this paper, we propose a systematic solution to extend the matrix computation of microring arrays from the real-valued field to the complex-valued field, and from small-scale (i.e., 4 x 4) to large-scale matrix computation (i.e., 16 x 16). Combining matrix decomposition and matrix partition, our photonic complex matrix-vector multiplier chip can support arbitrary large-scale and complex-valued matrix computation. We further demonstrate Walsh-Hardmard transform, discrete cosine transform, discrete Fourier transform, and image convolutional processing. Our scheme provides a path towards breaking the limits of complex-valued computing accelerator in conventional incoherent optical architecture. More importantly, our results reveal that an integrated photonic platform is of huge potential for large-scale, complex-valued, artificial intelligence computing and signal processing.