Physics-Based Analog Computing with Coupled Lasers for PDE and Optimization Problems

Many of today’s important computational science and engineering problems, such as solving partial differential equations (PDEs) and large-scale optimization tasks, require substantial computing resources and long runtimes on conventional digital hardware. LightSolver addresses such workloads by developing a new physics-based analog computing system that performs computation through the collective dynamics of interacting lasers inside an optical resonator, efficiently emulating other physical systems whose steady states encode the desired solutions. This approach aims to achieve faster and more energy-efficient computation for suitable classes of PDEs and optimization problems.

In LightSolver’s laser processing unit (LPU), instead of updating variables step by step in a digital processor, many optical degrees of freedom, such as the amplitude and phase of the electric field in each spatially separated laser in the array, evolve in parallel. By engineering gain, loss and optical coupling, the system realizes an effective loss landscape, or cost function, over these degrees of freedom, and its dynamics drive it toward low-loss configurations that encode good approximate solutions to the encoded problem, rather than necessarily the exact ground state.

In my talk, I will first explain how computation can be carried out on coupled-laser systems and what kinds of computations can be addressed with this approach. I will then show how this framework can be applied to PDEs and related optimization problems. In particular, I will explain how discretized PDEs, such as Poisson, diffusion and related equations, are mapped onto the coupled-laser system: differential operators and boundary conditions are translated into optical couplings and local terms, so that the laser array emulates the physics of another system whose steady state represents the solution of the original PDE.

I will then discuss optimization problems, showing how a range of spin models for NP-hard optimization tasks, including binary models (QUBO and Ising), XY spin models, and continuous formulations, can be represented on the platform. This enables a range of applications in optimization and points toward further uses in areas such as AI and cryptography. Finally, I will outline our LPU Lab, a cloud-accessible environment that allows researchers and students to experiment with these ideas directly on a coupled-laser system and its simulator, and I will demonstrate how the system is used in practice.