Computing matrix inversion with optical networks.

With this paper we bring about a discussion on the computing potential of complex optical networks and provide experimental demonstration that an optical fiber network can be used as an analog processor to calculate matrix inversion. A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber network containing three nodes and operating at telecomm wavelength. For an NxN matrix, the overall solving time (including setting time of the matrix elements and calculation time of inversion) scales as O(N(2)), whereas matrix inversion by most advanced computer algorithms requires ~O(N(2.37)) computational time. For well-conditioned matrices, the error of the inversion performed optically is found to be around 3%, limited by the accuracy of measurement equipment.