Retrieving space-dependent polarization transformations via near-optimal quantum process tomography

Abstract

An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator, whose action can be experimentally determined via quantum process tomography. Standard approaches to tomographic problems rely on the maximum-likelihood estimation, providing the most likely transformation to yield the same outcomes as a set of experimental projective measurements. The performances of this method strongly depend on the number of input measurements and the numerical minimization routine that is adopted. Here we investigate the application of genetic and machine-learning approaches to this problem, finding that both allow for more accurate reconstructions and faster operations when processing a set of projective measurements very close to the minimal one. We also apply these techniques to the case of space-dependent polarization transformations, providing an experimental characterization of the optical action of complex spin-orbit metasurfaces. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes, including non-unitary gates and operations in higher-dimensional Hilbert spaces.