Robustness Properties of Quantum Reservoir Computers

We investigate the robustness and scaling behavior of quantum reservoir computing (QRC) based on transverse-field Ising model (TFIM) dynamics. Motivated by the need for efficient information mixing and noise resilience, we construct reservoirs with expander-like connectivity—sparse graphs with high spectral gaps that emulate all-to-all coupling while maintaining local control. Using neutral-atom arrays as a model platform, we explore how connectivity degree, disorder, and noise shape computational performance. By sweeping the degree through the percolation threshold, we reveal a transition from localized to delocalized spin dynamics. This optimizes nonlinear memory capacity and predictive power near the "edge of chaos." Sparse expander topologies offer a favorable balance between expressivity and stability, maintaining predictive power even in the presence of both coherent and incoherent noise. These findings identify percolation and spectral expansion as key design principles for scalable, noise-resilient quantum machine-learning architectures grounded in many-body dynamics. They further underscore the intrinsic robustness of the reservoir computing paradigm across learning tasks.