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.

翻译：求解大规模稀疏线性系统是科学计算与工程仿真中的基础任务，通常主导着高性能计算应用中的运行时间与能耗。本研究探索了一种基于模拟光学处理的替代计算范式，通过激光处理单元（LPU）实现。该单元将线性系统编码至光学谐振腔内耦合激光器的动力学过程中，其中光场的稳态相位对应于方程$Ax=b$的解。我们提出了通用线性系统（包括稠密与稀疏类型）到LPU架构的映射方法，并利用SuiteSparse集合中的代表性矩阵评估其性能。通过LPU仿真器，我们针对稀疏多带状矩阵，将收敛行为与求解时间与现代GPU平台上的经典Krylov子空间方法（CG、GMRES、BiCGSTAB等）进行对比。实验结果表明，对特定问题类别，LPU将显著降低求解时间，揭示了光学模拟计算加速迭代线性求解器的潜力。这些发现表明，LPU等光学处理器可作为线性系统（尤其是结构化或需重复求解的线性系统）的加速器，在延迟、并行性与能效方面具备优势。我们讨论了当前限制（包括规模约束与精度考量），并展望了光-数字混合计算系统的发展方向。