Fig. 1. Experimental setup and the topological phase classifier.

a The structure of a nitrogen-vacancy center in a diamond crystal. The blue, yellow, and gray spheres represents vacancy, nitrogen, and carbon atoms, respectively. b The structure of 3D convolutional neural network (CNN) classifier. The input data are density matrices sampled from a 10 × 10 × 10 regular grid in the momentum space, and each density matrix is represented by three real indices among the Bloch sphere. With two 3D convolution (Conv3D) layers, one max pooling layer and one fully connected layer, the classifier outputs the probabilities P(χ = 0, 1, − 2) for each phase. c The potential limitation of the CNN classifier on data with random dropping. The classifier can correctly classify the clean data of topologically trivial phase (h = 3.2, χ = 0) with more than 80% of the data samples dropped, but the adversarial ratio (Adv. ratio) also increases as the dropping ratio increases. The error bars are obtained from 100 random data dropping trials. d The ratio of adversarial perturbations around the phase transition point. The random simulated perturbations are more likely to behave as adversarial perturbations when h approaches the transition point. Even when no data samples are dropped, the simulated perturbations may mislead the classifier. The situation becomes more serious when the dropping ratio increases to 20% and 40%. e The experimental procedure for the preparation and measurement of the ground states of the Hopf Hamiltonian at each momentum k. The dashed rectangle inserted before the final measurement represents a π/2 pulse with different phases. The directions of the electron spin on the Bloch sphere at three different time points are shown below the sequence.