a Mini-Circuits ZFSC-2-10G power splitter/combiner and sent to the cavity input line of the dilution refrigerator. The tone $\omega_{\rm q}$ is used for qubit characterization by two-tone spectroscopy with the drive tone turned off.

In the case of relaxation time measurements shown in Fig. \[fig:mschema\](b), we use the signal provided by the PNA-L network analyzer to drive the resonator and at the same time to provide a frequency reference for the mixer used for down-conversion. To create the microwave pulse applied to the qubit, we use an arbitrary waveform generator Tektronix AWG5014B. The pulse-shape signal created by this device is up-converted to the qubit frequency using a mixer and the local oscillator (LO) provided by the Agilent E8257D analog signal generator. As shown in Fig. 1(d) in the main text, we produce in this way a 2 $\mu\textrm{s}$-long microwave excitation pulse which is applied to the transmon gate line. The frequency $\omega_{\rm q}$ of this pulse is kept in resonance with the ac-Stark shifted transition frequency between the ground and first excited states of the transmon, which was measured separately. The incoming signal from the resonator is down-converted using an IQ mixer with the LO at $\omega_{\rm d}$, and then 