Integrated photonic multigrid solver for partial differential equations

Solving partial differential equations is crucial to analysing and predicting complex, large-scale physical systems but pushes conventional high-performance computers to their limits. Application specific photonic processors are an exciting computing paradigm for building efficient, ultrafast hardware accelerators. Here, we investigate the synergy between multigrid based partial differential equations solvers and low latency photonic matrix vector multipliers. We propose a mixed-precision photonic multigrid solver, that offloads the computationally demanding smoothening procedure to the optical domain. We test our approach on an integrated photonic accelerator operating at 2 GSPS solving a Poisson and Schr\"odinger equation. By offloading the smoothening operation to the photonic system, we can reduce the digital operation by more than 80%. Finally, we show that the photonic multigrid solver potentially reduces digital operations by up to 97 % in lattice quantum chromodynamics (LQCD) calculations, enabling an order-of-magnitude gain in computational speed and efficiency.