Gain-based computing utilizing non-Hermitian dynamics in light-matter interactions presents a novel approach to physics-based hardware and physics-inspired algorithms. By encoding complex optimization problems into the gain and loss rates of driven-dissipative systems, we leverage non-Hermiticity to destabilize non-optimal states and guide the system toward the global minimum. The incorporation of prior knowledge about ground state energies into the complex part of the energy enhances the system’s ability to navigate complex energy landscapes.

In this paradigm, the system undergoes symmetry-breaking transitions on a dynamically changing loss landscape, selecting modes that minimise losses and manifesting the optimal solutions to the original problems. This approach enables solving significant combinatorial optimization problems via mapping to Ising, XY, and k-local Hamiltonians, applicable across various physical platforms, including photonic, electronic, and atomic systems.

 Despite advancements, critical questions remain regarding scalability, the impact of phase space structures on system performance, and the identification of problems best suited for these unconventional computing architectures. I will address these challenges in my talk by understanding the dynamic behaviour during symmetry-breaking transitions, optimizing trajectories toward global minima, quantifying error probabilities, and using dissipation and nonlinearities to correct errors.