TL;DR: Still no "optical transistor" yet, but they figured out a way to do matrix multiplication:

The researchers encoded the various quantities they wanted to multiply into beams of light, then sent the beams through a series of components that altered the beam’s phase—the way its light waves oscillated—with each phase alteration representing a multiplication step. By repeatedly splitting the beams, changing their phase, and recombining them, they could make the light effectively carry out matrix multiplication. At the end of the chip, the researchers placed photo detectors that measured the light beams and revealed the result.