PhotoSolver: A bidirectional photonic solver for systems of linear equations

Abstract

Solving systems of linear equations is one of the most fundamental challenges in computing, with ubiquitous applications in science and engineering. Solving large-scale linear equations is particularly challenging, requiring tremendous computing expenses. However, conventional solvers in electronic digital computers face inevitable physical bottlenecks that hinder further advancements in electronic chips. Unlike the electronic architectures, optical computing harnesses the inherent advantages of lights, such as ultimately high speed, negligible energy consumption, and high parallelism, making optical architectures attractive sources for ultra-high speed analog computing. Especially, recent advances in integrated photonic circuits bring exciting new possibilities for high performance computing based on photonic chips. In this work, we propose a bidirectional PhotoSolver using the propagation of optical signals in different directions on a single integrated photonic chip to perform multiple operations in solving systems of linear equations, scalable to solve large-scale systems. Specifically, we propose an in situ approach to iteratively update solutions by performing the forward and backward propagations within a single photonic chip. Furthermore, we propose a partitioning approach to solve large-scale systems using arrays of photonic chips. Numerical experiments demonstrate these capabilities with representative systems of linear equations. By utilizing lights propagating in integrated photonic chips, our PhotoSolvers provide a promising computing architecture to solve large systems of linear equations, with potentials in wide computational applications.