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

TL;DR

This paper explores advanced quantum process tomography techniques, including machine learning, to efficiently characterize space-dependent polarization transformations in optical systems, with potential for real-time applications.

Contribution

It introduces machine learning and genetic algorithms to improve the speed and accuracy of quantum process tomography for optical polarization transformations.

Findings

Neural network-based tomography significantly speeds up the process.

Both genetic and machine learning methods achieve accurate reconstructions with minimal measurements.

The approach is effective for characterizing complex spin-orbit metasurfaces.

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 accurate reconstructions and fast operations when processing a set of projective measurements very close to the minimal one. We apply these techniques to the case of space-dependent polarization transformations, providing an experimental characterization of the optical action of spin-orbit metasurfaces having patterned birefringence. Our efforts thus expand the toolbox of methodologies for optical process tomography. In particular, we find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. 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.