Experimental demonstration of adversarial examples in learning topological phases

Classification and identification of different phases and the transitions between them is a central task in condensed matter physics. Machine learning, which has achieved dramatic success in a wide range of applications, holds the promise to bring unprecedented perspectives for this challenging task. However, despite the exciting progress made along this direction, the reliability of machine-learning approaches in experimental settings demands further investigation. Here, with the nitrogen-vacancy center platform, we report a proof-of-principle experimental demonstration of adversarial examples in learning topological phases. We show that the experimental noises are more likely to act as adversarial perturbations when a larger percentage of the input data are dropped or unavailable for the neural network-based classifiers. We experimentally implement adversarial examples which can deceive the phase classifier with a high confidence, while keeping the topological properties of the simulated Hopf insulators unchanged. Our results explicitly showcase the crucial vulnerability aspect of applying machine learning techniques in experiments to classify phases of matter, which can benefit future studies in this interdisciplinary field.