Device variability of Josephson junctions induced by interface roughness

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${\text{x}}$/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${\text{x}}$ 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.

💡 Research Summary

The paper addresses a pressing issue for scalable superconducting quantum processors: device‑to‑device variability arising from microscopic imperfections in Al/AlOₓ/Al Josephson junctions. Because the critical current I_c (and thus the Josephson energy E_J) depends exponentially on the tunnel‑barrier thickness, even nanometer‑scale fluctuations can cause significant spread in qubit frequencies and gate fidelities. The authors develop a quantitative framework that links interface roughness to the statistical distribution of E_J.

First, the Al/AlOₓ interfaces are modeled as Gaussian random fields with zero mean and an autocorrelation function ⟨h(x,y)h(0,0)⟩ = σ² exp