  The characterization of a unitary gate is experimentally accomplished via
Quantum Process Tomography, which combines the outcomes of different projective
measurements to reconstruct the underlying operator. The process matrix is
typically extracted from maximum-likelihood estimation. Recently, optimization
strategies based on evolutionary and machine-learning techniques have been
proposed. Here, we investigate a deep-learning approach that allows for fast
and accurate reconstructions of space-dependent SU(2) operators, 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 on
complex polarization transformations. Our approach further expands the toolbox
of data-driven approaches to Quantum Process Tomography and shows promise in
the real-time characterization of complex optical gates.
