Extended Data Fig. 2: Noise floor of HOM experiment.

a, Data shown in Fig. 1b in log scale, here without visibility correction (see Methods). For the single-phonon splitting experiment, we expect at most one excitation during the entire process. The ideal P_ee is zero for the duration of the experiments, and in particular, it should be zero after 650 ns, when each qubit has completed its capture of the split single-phonon wavepacket. We attribute the non-zero P_ee population after that time to residual qubit thermal excitations and readout errors. We display the mean P_ee population P_ee,floor = 0.0014 ± 0.0005 from 650 to 800 ns (dashed gray line, with uncertainty represented by the shaded area). We note the cryostat base temperature is 7 mK, but Q₂ starts with a spurious (thermal-like) population of around 0.4%, which we can convert to an effective temperature of 35 mK. When interacting with the phonon channel, Q₂ gradually cools to an excited state population of 0.2% or an equivalent temperature of about 31 mK. As Q₂’s excitation after catching the half-phonon wavepacket is 32%, this spurious population contributes roughly ~ 0.002 × 0.32 = 6.4 × 10⁻⁴ to the P_ee background. A similar estimate for Q1 gives a total background of ~ 1.3 × 10⁻³ to P_ee, which is close to our measured background of 0.0014 ± 0.0005. b, Data shown in Fig. 1d together with P_Q1 and P_Q2 in log scale, again here without visibility correction. The two-phonon interference experiments use a pulse sequence similar to that for the single-phonon experiments, and the final populations for P_Q1 and P_Q2 are close to those for the single-phonon experiments¹³. We observe P_ee is suppressed near τ = 0, and at τ = 0 it is consistent with the baseline noise floor P_ee,floor. We thus believe P_ee,floor is a reasonable estimate for the noise floor in this experiment.