While physical reservoir computing is a promising way to achieve low power consumption neuromorphic computing, its computational performance is still insufficient at a practical level. One promising approach to improving its performance is deep reservoir computing, in which the component reservoirs are multi-layered. However, all of the deep-reservoir schemes reported so far have been effective only for simulation reservoirs and limited physical reservoirs, and there have been no reports of nanodevice implementations. Here, as an ionics-based neuromorphic nanodevice implementation of deep-reservoir computing, we report a demonstration of deep physical reservoir computing with maximum of four layers using an ion gating reservoir, which is a small and high-performance physical reservoir. While the previously reported deep-reservoir scheme did not improve the performance of the ion gating reservoir, our deep-ion gating reservoir achieved a normalized mean squared error of 9.08 × 10−3 on a second-order nonlinear autoregressive moving average task, which is the best performance of any physical reservoir so far reported in this task. More importantly, the device outperformed full simulation reservoir computing. The dramatic performance improvement of the ion gating reservoir with our deep-reservoir computing architecture paves the way for high-performance, large-scale, physical neural network devices.