Optimization plays a crucial role in making decisions and in analyzing systems. Specifically, it deals with finding the best solution from among many feasible solutions (for example traveling salesman problem). Such problems are ubiquitous across social science, biology, chemistry, physics, engineering, computer science, big data and artificial intelligence. Many such problems are classified as computationally hard problems, and solving them efficiently and rapidly with physical systems has become an emerging field of research. Physical optimization relies on finding the ground state of a complex system as a physical analogy to the optimization problem.

Coupled lasers can rapidly and efficiently dissipate into a stable phase locked state that can be mapped onto the minimal energy state of spin Hamiltonian. In this talk, I will present a rapid laser solver based on coupled lasers for solving computationally hard problems, for example, object reconstruction from its scattered intensity distribution (phase retrieval problem) as well as statistical fair sampling of ground state manifold of XY spin Hamiltonian. Further, I will also discuss rapid and efficient formation of very high-resolution arbitrary shaped complex laser modes inside a digital degenerate cavity laser.