Extended Data Fig. 3: Qubit frequency tracking.

a, Raw qubit-tracking spectrum, obtained at 1 h elapsed time. First, the bare qubit spectrum is averaged over a 20-s interval, with a full spectral measurement performed every about 1 ms; all of the raw 20-s tracking spectra taken during the hour-long experiment are overlaid (grey circles). Then, these spectra are averaged without post-processing to obtain the effective bare qubit spectrum (green curve), resulting in an effective linewidth of about 2.8 MHz. b, Qubit-tracking spectrum with post-processing. The same qubit spectra as in a, but each 20-s tracking spectrum is aligned to the average qubit frequency using post-processing peak detection. The effective qubit linewidth is now improved to about 1.1 MHz. c, Alignment of bare qubit spectra through time. Each horizontal slice represents a 20-s tracking spectrum, showing that the qubit drifts by ±1.5 MHz during the experiment. d, Raw phonon-number-splitting spectrum. We interleave phonon-number-splitting measurements between the tracking spectra shown in a, alternating between the two every about 0.5 ms. When all of the raw spectra (grey points) are averaged without frequency correction (green curve), phonon-number splitting is visible but the peaks are poorly resolved. e, Post-processed phonon-number-splitting spectrum. Using the frequency corrections applied in b, we adjust the frequencies of each slice and improve the resolution of the peaks. f, Alignment of phonon-number-splitting spectra through time. The zero- and one-phonon peaks are easily visible with a splitting of 2χ ≈ 3 MHz.