I/O-efficient iterative matrix inversion with photonic integrated circuits

Abstract: Photonic integrated circuits have been extensively explored for optical processing with the aim of breaking the speed bottleneck of digital electronics. However, the input/output (IO) bottleneck remains one of the key barriers. Here we report a novel photonic iterative processor (PIP) for matrix-inversion-intensive applications. The direct reuse of inputted data in the optical domain unlocks the potential to break the IO bottleneck. We demonstrate notable IO advantages with a lossless PIP for real-valued matrix inversion and integral-differential equation solving, as well as a coherent PIP with optical loops integrated on-chip, enabling complex-valued computation and a net inversion time of 1.2 ns. Furthermore, we estimate at least an order of magnitude enhancement in IO efficiency of a PIP over photonic single-pass processors and the state-of-the-art electronic processors for reservoir training tasks and MIMO precoding tasks, indicating the huge potential of PIP technology in practical applications.