Fig. 4: Qubit frequency variability and ageing analysis.

a, RSDs of qubit frequencies and normal state resistances of JJ test structures (\({{\rm{RSD}}}_{{f}_{{\rm{qb}}}}={{\rm{RSD}}}_{{R}_{{\rm{n}}}}/2\), visualized with the double y axes) as a function of the estimated JJ area. 9 (qubits per die) × 24 (dies) = 216 qubits across the wafer, 8 (JJs per area per die) × 12 (areas) × 82 (dies) = 7,872 JJs across a wafer, 146 (JJs per area) × 12 (areas) = 1,752 JJs on a die (0,2). All working qubits are included. The resistances of JJ test structures were filtered per area for outliers beyond 1.5 times the interquartile range. Solid lines are fits to equation (2). b, Normal resistances of JJ test structures as a function of estimated junction area for a subgroup of 216 devices measured 5 days after fabrication (t₀) and once more 146 days after fabrication. The right y axis shows the corresponding change in the relative average resistance for each JJ area. c, Wafer map of qubit frequencies scaled with \(\sqrt{A}\) (where A is the estimated JJ area) and ensemble averaged (⟨⟩_e) over the nine qubits on each subdie D2. The mean values are accompanied by the standard deviation. The background colour represents a heuristic Gaussian fit to the average value as a function of radius. d, Area-scaled qubit frequencies of qubits on subdies D2 plotted as a function of cool-down time after fabrication, compared with the product of the resistance and area of the JJs extracted from the fits in b scaled with a proportionality factor \(X\approx \sqrt{\varDelta {E}_{{\rm{C}}}/h{e}^{2}}\) (where Δ is the superconducting gap of aluminium, E_C is the qubit charging energy, h is Planck’s constant and e is the elementary charge). The black vertical dashed line represents the wafer fabrication date at t₀. Distributions of measured qubits are represented by violin plots showing means and extrema. The grey area indicates the ageing from JJ data.