A method for finding the background potential of quantum devices from scanning gate microscopy data using machine learning

The inverse problem of estimating the background potential from measurements of the local density of states is a challenging issue in quantum mechanics. Even more difficult is to do this estimation using approximate methods such as scanning gate microscopy (SGM). Here, we propose a machine-learning-based solution by exploiting adaptive cellular neural networks (CNNs). In the paradigmatic setting of a quantum point contact, the training data consist of potential-SGM functional relations represented by image pairs. These are generated by the recursive Green's function method. We demonstrate that the CNN-based machine learning framework can predict the background potential corresponding to the experimental image data. This is confirmed by analyzing the estimated potential with image processing techniques based on the comparison between the charge densities and those obtained using different techniques. Correlation analysis of the images suggests the possibility of estimating different contributions to the background potential. In particular, our results indicate that both charge puddles and fixed impurities contribute to the spatial patterns found in the SGM data. Our work represents a timely contribution to the rapidly evolving field of exploiting machine learning to solve difficult problems in physics.