Abstract
As quantum processors scale to large qubit numbers, device-to-device variability emerges as a critical challenge. Superconducting qubits are commonly realized using Al/AlO_x/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 E_J induced by interface roughness at the Al/AlO_x 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 5,000 Josephson junctions show that E_J follows a log-normal distribution. The mean value of E_J increases with σ and decreases slightly with ξ , while the variance of E_J 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.