As quantum processors scale to large qubit numbers, device-to-device variability emerges as a critical challenge. Superconducting qubits are commonly realized using Al/AlOx/Al Josephson junctions operating in the tunneling regime, where even minor variations in device geometry can lead to substantial performance fluctuations. In this work, we develop a quantitative model for the variability of the Josephson energy EJ induced by interface roughness at the Al/AlOx interfaces. The roughness is modeled as a Gaussian random field characterized by two parameters: the root mean square roughness amplitude σ and the transverse correlation length ξ. These parameters are extracted from the literature and molecular dynamics simulations. Quantum transport is treated using the Ambegaokar–Baratoff relation combined with a local thickness approximation. Numerical simulations over 5000 Josephson junctions show that EJ follows a lognormal distribution. The mean value of EJ increases with σ and decreases slightly with ξ, while the variance of EJ increases with both σ and ξ. These results paint a quantitative and intuitive picture of Josephson energy variability induced by surface roughness, with direct relevance for junction design.
Zhu et al. (Mon,) studied this question.