Ranges of the Josephson harmonics ratios | E J m / E J1 | that are consistent with the measured spectra. The ranges are represented by coloured vertical bars using the same colouring as in a . For the IBM Hanoi device, we show the ranges for qubits 0–2 from left to right (ranges for the other qubits are shown in Supplementary Section IC3 ). The shaded grey area highlights the region between two limiting cases: the fully open quantum point contact with unit transparency and a homogeneous barrier with T n = 10 −6 for all n . Turquoise markers on the vertical bars indicate the harmonics ratios calculated from the mesoscopic model, where the average thickness \bar{d} and the standard deviation σ are given in b . Inset, an Al–AlO x –Al junction obtained from molecular dynamics simulations (Supplementary Fig. 25 ) with average barrier thickness \bar{d}=1.5 {{\rm{nm}}} (Fig. 2c ).
