Figure 3: T₁ variation with qubit frequency and noise modelling.

(a) Energy-relaxation time T₁ versus qubit frequency for Qubit C (C_sh,C=9 fF, I_p,C=275 nA, Δ_c/2π=0.82 GHz) plotted with simulated T₁ values for individual (dashed lines) and aggregate (solid line) charge, flux and Purcell noise mechanisms. Absence of data around 4 GHz is related to an ancillary qubit level crossing the readout resonator, prohibiting qubit readout and is not a systematic issue. Qubit C is limited by flux noise below about 4.5 GHz. For comparison, the functional form for ohmic flux noise (grey dotted line) is incompatible with the data below 3 GHz; above 3 GHz, its role cannot be readily distinguished from charge noise (see text). Shaded region indicates the range of predicted T₁ in the presence of 0–1.0 quasiparticles. (b) Flux noise spectroscopy performed on Qubit B using Ramsey interferometry (red) and T_1ρ spin-locking (blue) to determine parameters A_Φ²=(1.4 μΦ₀)²/Hz and γ =0.9 for the inverse-frequency flux noise (black dashed line) for qubit C (a). Green and black dots: inferred ohmic flux noise S_Φ based on measured T₁ in a. (c) Energy-relaxation time T₁ versus qubit frequency for qubit B (C_sh,B=51 fF, I_p,B=49 nA, ). T₁ is sensitive predominantly to ohmic charge noise within 5–6.5 GHz range. Scatter in T₁ is attributed to quasiparticle fluctuations. Cluster of lower T₁ values near 5.5 GHz is due to interaction with the f₁₂ transition. Shaded region indicates the range of predicted T₁ in the presence of 0–1.0 quasiparticles. (d) T₁ values for 22 qubits with widely varying design parameters, measured at their degeneracy points and plotted against predicted T₁ values (dashed line) determined from numerical simulations using a single model with fixed noise levels (see main text). Practically indistinguishable data points (eight in total) are indicated with arrows.