Systematic errors in the calibration of cryogenic amplifier chains due to Fano interference

Waveguide-QED transmon measurements are a powerful tool to calibrate microwave amplification chains inside a dilution refrigerator. Here we show how systematic errors of up to 2 dB on the extracted added noise arise from Fano interference of the signal with a background path. Limited knowledge of the interfering paths in a given setup translates into a range of uncertainty for the added noise calibration, which increases with the transmon-waveguide coupling strength. We experimentally illustrate the relevance of Fano interference in calibrating using a waveguide-QED transmon as a power sensor and quantify the errors encountered in extracting amplifier noise parameters. We also show how to characterize and utilize the Fano interference to eliminate these systematic errors.