Machine learning the Biot-Savart law from quantum sensor data

We use a supervised neural network to reconstruct current distributions from magnetic field maps provided by a quantum diamond microscope (QDM). The neural network employs a U-Net architecture. We train the network with more than 10⁴ simulated and real training data sets consisting of QDM magnetic images of 2D patterns of current-carrying wires. We find that the trained network can reproduce with high fidelity a heretofore unseen current distribution from the associated QDM magnetic image, thereby learning the Biot-Savart law. We anticipate that this Q4ML technology (quantum data for machine learning) will have wide-ranging applications, including the study of hydrodynamic electron flow in graphene, activity within integrated circuits, and electrical activity in biological systems.