Tomography and characterization of harmonic oscillator systems*

Quantum state reconstruction is an important element enabling diagnosis and improvement of quantum control. As larger states are controlled, care needs to be taken to mitigate experimental imperfections and the number of measurements required to perform state reconstruction becomes crucial. Significant gains can be found by choosing the appropriate basis in which to make measurements. In this talk I will discuss experimental techniques to characterize extended quantum harmonic oscillator states, focusing on measurements of the Wigner characteristic function. The latter allowed for a factor of 20 improvement in measurement time for the reconstruction of the motional state of a trapped ion [1] and enabled tomography of a microwave resonator weakly coupled to a transmon qubit [2].
[1]: C. Flühmann et al. PRL 125, 043602 (2020)
[2]: P. Campagne-Ibarcq et al. Nature 584, 368-372 (2020)