  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.
