Quadratic Optimization with Integrated Photonics

Abstract

We investigate the feasibility of building a fast quadratic optimizer using integrated photonics. We nd that a relatively simple analog for a linear hop eld neuron can be implemented using integrated photonic components. Utilizing the solution of the hop eld energy equation for a linear hop eld network, we show that our network can be used minimize quadratic functions of n variables. Using a time based device simulation, we demonstrate that the integrated optical network does indeed converge to the minima of quadratic functions in < 15ns with an average error of 0:5% or below. We discuss potential applications of this device from compressed sensing to multivariate least squares regression, as well as applications which would be made possible if the device were to be augmented so that it could minimize a quadratic function subject to linear inequality constraints.