Fig. 2: Flow chat of recognizing the multifrequency MWs and results.

a Process of encoding and decoding frequency-division multiplexed binary phase-shift keying (FDM-2PSK) signal with Rydberg atoms and the deep learning model. b, c Loss curve evolution with epochs for the training set (blue) and the validation set (orange) during training with different training data and validation data. The training data sizes are b 393 and c 1194. The validation data sizes are b 131 and c 398; more details about the data set split are presented in the “Methods” section. The loss curves for training and validation converge at b 140 and c 30 epochs, where an epoch is a time unit during which the model iterates once over the complete data set; see “Methods” section. d Confusion matrix for a test set (the number of the testing set is 160 and the labels are uniformly distributed) after training in case (c). The accuracy reaches 99.38% after a 70-epoch training period. e Deep learning model accuracy on the noisy test set after training on the noisy training set. The x- and y-axes represent the standard deviations of the additional white noise added to the test set and the training set, respectively. The colorbar represents the accuracy of the model on the noisy test set. The results were obtained by averaging five sets of predictions. The diagonal (red line) indicates the accuracy of the model on a test set in which the noise distribution is the same as that of the training set; more details about the noise are shown in Supplementary Materials.