Experimental machine learning quantum homodyne tomography

Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, this task becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to experimental balanced homodyne tomography and show it to allow full estimation of quantum states based on a smaller amount of experimental data. Although our experiment is in the optical domain, our method provides a way of exploring quantum resources in a broad class of physical systems, such as superconducting circuits, atomic and molecular ensembles, and optomechanical systems.