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

Photonic integrated circuits have been explored extensively for optical processors with the aim of breaking the speed bottleneck of digital electronics in special-purpose tasks. Here we report a novel photonic iterative processor (PIP) for matrix inversion that underpins a wide range of scientific and engineering problems. A direct reuse of inputted data in the optical domain unlocks the potential to break the input/output bottleneck, which is regarded as one of the key barriers for optics to gain real benefits over electronics for computing. We demonstrate a lossless PIP for real-valued matrix inversion and use it to solve integral and differential equations. We further demonstrate a coherent PIP with optical loops integrated on-chip, enabling complex-valued computation and a net inversion time of 900ps. With much less demand for data movement among compute and memory units, at least an order of magnitude computation speed enhancement by using such a PIP over a single-pass optical processor is estimated for ridge regression task in both house price prediction and MNIST training.