Disentangling memory and nonlinearity in time-multiplexed optical reservoir computing

We analyze and disentangle the individual and combined roles of nonlinearity, transient dynamics, and delayed feedback and investigate how these mechanisms contribute to different task requirements in photonic reservoir computing. This is achieved using a passive linear photonic reservoir in which a photodiode at the optical-to-electrical interface provides the sole source of nonlinearity. We demonstrate how the requirements of different tasks can be quantified and compared to the dynamics provided by the reservoir by explicitly calculating and comparing the contributing monomials. Our findings show that a reservoir with uncoupled virtual nodes and a quadratic nonlinearity can already achieve good performance for tasks derived from dynamical systems with quadratic nonlinearities, such as the Lorenz63 system. Furthermore, transient coupling and delayed feedback significantly enhance the computational capabilities by compensating for missing higher-order monomials through an effective multi-step integration scheme, given the minimum nonlinearity required for the task is present in the reservoir.