Process tomography of structured optical gates with convolutional neural networks

Efficient and accurate characterization of an experimental setup is a critical requirement in any physical setting. In the quantum realm, the characterization of an unknown operator is experimentally accomplished via Quantum Process Tomography (QPT). This technique combines the outcomes of different projective measurements to reconstruct the underlying process matrix, typically extracted from maximum-likelihood estimation. Here, we exploit the logical correspondence between optical polarization and two-level quantum systems to retrieve the complex action of structured metasurfaces within a QPT-inspired context. In particular, we investigate a deep-learning approach that allows for fast and accurate reconstructions of space-dependent SU(2) operators by only processing a minimal set of measurements. We train a convolutional neural network based on a scalable U-Net architecture to process entire experimental images in parallel. Synthetic processes are reconstructed with average fidelity above 90%. The performance of our routine is experimentally validated in the case of space-dependent polarization transformations acting on a classical laser beam. Our approach further expands the toolbox of data-driven approaches to QPT and shows promise in the real-time characterization of complex optical gates.