A remarkable phenomenon in contemporary physics is quantum scarring in systems whose classical dynamics are chaotic, where certain wave functions tend to concentrate on classical periodic orbits of low periods. Quantum scarring has been studied for more than four decades, but detecting quantum scars still mostly relies on human visualization of the wave-function patterns. The widespread and successful applications of machine learning in many branches of physics suggest the possibility of using artificial neural networks for automated detection of quantum scars. Conventional machine learning often requires substantial training data, but, for quantum scars, this poses a significant challenge: in typical systems the available distinct quantum scarring states are rare. We develop a meta machine-learning approach to accurately detect quantum scars in a fully automated and highly efficient fashion. In particular, taking advantage of some standard large datasets such as Omniglot from the field of image classification, we train a “preliminary” version of the neural network that has the ability to distinguish different classes of noisy images. We then perform few-shot classification to further train the neural network but with a small number of quantum scars. We demonstrate that the meta-learning scheme can find the correct quantum scars from thousands of images of wave functions without any human intervention, regardless of the symmetry of the underlying system. From a general applied point of view, our success opens the door to exploiting meta learning for solving challenging image detection and classification problems in other fields of science and engineering. For example, in microlasing systems, identifying scarring states is critical as these states are desired for directional emission. The task is also important for quantum-dot devices where the scarring states can lead to resonances in the conductance.

• Received 4 November 2022
• Revised 14 February 2023
• Accepted 18 May 2023

DOI:https://doi.org/10.1103/PhysRevApplied.19.064042