Supervised learning of the Jaynes-Cummings Hamiltonian

We investigate the utility of deep neural networks (DNNs) in estimating the Jaynes-Cummings Hamiltonian's parameters from its energy spectrum alone. We assume that the energy spectrum may or may not be corrupted by noise. In the noiseless case, we use the vanilla DNN (vDNN) model and find that the error tends to decrease as the number of input nodes increases. The best-achieved root mean squared error is of the order of [Formula: see text]. The vDNN model, trained on noiseless data, demonstrates resilience to Gaussian noise, but only up to a certain extent. To cope with this issue, we employ a denoising U-Net and combine it with the vDNN to find that the new model reduces the error by up to about 77%. Our study exemplifies that deep learning models can help estimate the parameters of a Hamiltonian even when the data is corrupted by noise.