We consider probe-based quantum thermometry and show that machine classification can provide model-independent estimation with quantifiable error assessment. Our approach is based on the $k$-nearest-neighbor algorithm. The machine is trained using data from either computer simulations or a calibration experiment. This yields a predictor which can be used to estimate the temperature from new observations. The algorithm is highly flexible and works with any kind of probe observable. It also allows one to incorporate experimental errors, as well as uncertainties about experimental parameters. We illustrate our method with an impurity thermometer in a Bose gas, as well as in the estimation of the thermal phonon number in the Rabi model.

• Received 20 July 2021
• Accepted 27 January 2022

DOI:https://doi.org/10.1103/PhysRevA.105.022413