Accelerating Sparse Linear Solvers with an Optical Laser Processing Unit

TL;DR

This paper investigates the use of an optical laser processing unit (LPU) to accelerate the solution of large, sparse linear systems, demonstrating potential advantages over traditional digital methods in speed and energy efficiency.

Contribution

It introduces a novel optical computing architecture for solving linear systems, mapping general matrices onto the LPU, and benchmarks its performance against GPU-based methods.

Findings

LPU can achieve lower time-to-solution for certain sparse matrices.

Optical processing offers advantages in latency, parallelism, and energy efficiency.

Benchmarking shows promising results compared to Krylov subspace methods.

Abstract

Solving large, sparse linear systems is a fundamental workload in scientific computing and engineering simulations, often dominating runtime and energy consumption in high-performance computing (HPC) applications. In this work, we explore an alternative computing paradigm based on analog optical processing, implemented through the Laser Processing Unit (LPU). The LPU encodes linear systems into the dynamics of coupled lasers within an optical cavity, where the steady-state phases of the optical fields correspond to the solution of $Ax=b$. We present a mapping of general linear systems, both dense and sparse, onto the LPU architecture and evaluate its performance using representative matrices from the SuiteSparse collection. Using an LPU emulator, we benchmark convergence behavior and time-to-solution for sparse, multi-banded matrices against established Krylov subspace methods (CG, GMRES, BiCGSTAB, and others) executed on a modern GPU platform. Our results demonstrate that the LPU will achieve significantly lower time-to-solution for selected problem classes, highlighting the potential of optical analog computing for accelerating iterative linear solvers. These findings suggest that optical processors such as the LPU will be able to serve as accelerators for linear systems, in particular structured and/or repeatedly solved, offering advantages in latency, parallelism, and energy efficiency. We discuss current limitations, including scaling constraints and precision considerations, and outline directions toward hybrid optical-digital computing systems.