Reconstructing Quantum Potentials from Magnetotransport Fingerprints via Automatic Differentiation

Mesoscopic and nanoscale semiconductor conductors exhibit reproducible, sample-specific fluctuations in magnetoconductance, often referred to as quantum fingerprints. These intricate patterns arise from the interference of electron waves scattered by the internal potential landscape of the sample. As such, the quantum fingerprint implicitly encodes detailed information about the underlying potential, though decoding this information is highly nontrivial. Recently, a generative neural network successfully reconstructed potential profiles from quantum fingerprints [1], but the approach was limited to systems of two quantum dots. Here, we propose a simple yet powerful framework to solve this class of inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined in the vicinity of the true solution and a numerical simulator is available. We demonstrate that the approach accurately reconstructs spatial potential profiles in mesoscopic conductors from magnetotransport measurements. The framework is general, flexible, and readily adaptable to a wide range of inverse problems in condensed matter physics and related fields.