Chip-scale optical matrix computations for PageRank algorithm

Matrix computations are indispensable tools in science and engineering, while the electronic matrix computations suffered from limited speed. Alternatively, the optical methods offered a high-speed solution. The optical matrix computation is impractical unless it is capable of extending to a large scale, reconfiguring for a general purpose and operating with high efficiency. Here, we report and experimentally demonstrate an optical matrix computing processor based on an integrated linear optical network. The proposed photonic processor is capable of performing fundamental matrix computations including $XB=C$ , $AB=X$ and $AX=C$ , where $A$ , $B$ , $C$ are known matrices, and $X$ is the matrix to be solved. An optical PageRank algorithm is further demonstrated based on the matrix computing processor for the first time. Our demonstration offers an optical method to achieve matrix computations and PageRank algorithm. Meanwhile, it suggests great potential for chip-scale fully programmable matrix computations with self-configuring methods.