Quantum Computer Flaws Mapped with New Roughness Model for Stable Processing

Researchers are increasingly focused on understanding device-to-device variability as quantum processors grow in complexity. Yu Zhu, Félix Beaudoin, and Hong Guo from Nanoacademic Technologies Inc. and the Department of Physics at McGill University have investigated the impact of interface roughness on Josephson junctions, fundamental components in many quantum computing architectures. Their work presents a quantitative model demonstrating how roughness at the Al/AlO interfaces induces fluctuations in Josephson energy, a critical performance parameter. By modelling roughness as a Gaussian random field and utilising the Ambegaokar, Baratoff relation, the team reveals a clear relationship between roughness parameters and the resulting variability, offering valuable insight for optimising junction design and improving the reliability of future quantum circuits.

As these processors scale to include increasing numbers of qubits, variations in device characteristics present a significant obstacle to achieving stable and reliable operation.

This work addresses this challenge by focusing on the variability of the Josephson energy, a critical parameter determining qubit behaviour, and its connection to microscopic roughness at the aluminium/aluminium oxide interfaces within the junctions. Through a combination of quantum transport theory, Gaussian random field modelling, and molecular dynamics simulations, the study establishes a direct link between the microstructural disorder of these interfaces and the resulting statistical distribution of Josephson energies.

The research models interface roughness using a Gaussian random field defined by the root-mean-square roughness amplitude, σ, and the transverse correlation length, ξ. Parameters for these values were obtained from existing literature and molecular dynamics simulations, allowing for a detailed analysis of their influence on junction performance.

Numerical simulations, performed on a population of 5,000 Josephson junctions, reveal that the Josephson energy follows a log-normal distribution. The mean value of this energy increases with both σ and ξ, while the variance increases with both parameters, providing an intuitive understanding of how surface roughness affects junction variability.

These findings are directly relevant to the design of Josephson junctions, offering insights into optimising fabrication processes to minimise unwanted fluctuations in qubit characteristics. By accurately predicting the statistical distribution of Josephson energies, this model enables more precise control over qubit frequency and gate fidelity, paving the way for larger, more stable, and ultimately more powerful superconducting quantum computers. The ability to quantitatively link microscopic interface disorder to macroscopic junction behaviour represents a significant step towards overcoming a key limitation in scaling quantum processors towards the millions of qubits needed for complex computations.

Modelling Josephson energy variability via Gaussian random field simulations provides insights into critical current distributions

A 72-qubit superconducting processor forms the foundation of this work, enabling quantitative modelling of Josephson junction variability induced by interface roughness. Researchers addressed the critical challenge of device-to-device variability in superconducting circuits by focusing on Al/AlOₓ/Al Josephson junctions, where minor geometric variations significantly impact performance.

The study developed a quantitative model for Josephson energy variability, modelling interface roughness as a Gaussian random field defined by a root-mean-square roughness amplitude and a transverse correlation length. These parameters were extracted from existing literature and molecular dynamics simulations to accurately represent the physical characteristics of the junctions.

Quantum transport calculations were performed using the Ambegaokar, Baratoff relation, combined with a local thickness approximation to simplify the complex simulations. Numerical simulations across numerous Josephson junctions demonstrated that the Josephson energy follows a log-normal distribution, providing statistical insight into its fluctuations.

The mean value of the Josephson energy increased with both the roughness amplitude and the correlation length, while its variance increased with both parameters, revealing the interplay between these factors. This detailed analysis provides an intuitive understanding of how surface roughness affects junction design.

To overcome computational limitations posed by realistic junction dimensions, approximately 100nm × 100nm × 1nm, and the Fermi wavelength of aluminium, which is around 3.6 Å, the research team implemented two key approximations. First, the Ambegaokar, Baratoff relation was used to relate the critical current to the normal resistance, simplifying the calculation and reducing the system size by considering only electron-like quasiparticles.

Validation against direct solution of the Bogoliubov, de Gennes equation confirmed the accuracy of this approach over a wide range of junction thicknesses, justifying its use throughout the study. Second, transport direction was separated from transverse directions, leveraging the tunneling regime to approximate the total normal conductance as a sum of independent transverse subsystems.

This local thickness approximation was justified by comparing characteristic length scales: the Fermi wavelength, the wavefunction decay length in the tunnel barrier, the RMS interface roughness, and the correlation length of the roughness. Since the change in tunnel barrier thickness over a lateral distance was significantly smaller than the decay length, the barrier was treated as an ensemble of locally uniform barriers. The interface roughness model and quantum transport framework were combined to study the variability of the Josephson energy in Al/AlOₓ/Al junctions, modelling the junction as metallic leads separated by a three-dimensional tunnel barrier with a height of approximately 1 eV, a width of around 1nm, and a cross section of 200nm × 200nm.

Josephson energy distribution correlates with interfacial roughness parameters as expected

Numerical simulations encompassing 5,000 Josephson junctions reveal that the Josephson energy, EJ, follows a log-normal distribution. The mean value of EJ increases with the root-mean-square roughness amplitude, σ, while decreasing slightly with the transverse correlation length, ξ. Furthermore, the variance of EJ increases with both σ and ξ, demonstrating a clear relationship between interfacial roughness and energy variability.

These findings provide a quantitative and intuitive understanding of how surface roughness induces fluctuations in Josephson energy, directly informing junction design. The research models interface roughness as a Gaussian random field, defined by the root-mean-square roughness amplitude, σ, and the transverse correlation length, ξ.

Parameters σ and ξ were extracted from existing literature and molecular dynamics simulations to accurately represent the physical characteristics of the Al/AlOx interfaces. Quantum transport was then evaluated using the Ambegaokar, Baratoff relation in conjunction with a local thickness approximation, allowing for detailed analysis of junction behavior.

Analysis of the generated rough interfaces indicates that the transverse correlation length, ξ, is closely linked to the lateral grain size of the aluminum leads, with observed grain sizes ranging from approximately 20nm x 30nm to 900nm or even 1μm depending on deposition conditions. Experimental studies report mean AlOx thicknesses between 1.66nm and 1.88nm, with standard deviations ranging from 0.326nm to 0.372nm, suggesting a representative range for σ of approximately 0.1nm to 0.3nm.

Molecular dynamics simulations were also employed to estimate σ, complementing the experimentally derived values. These combined results establish a direct connection between microstructural disorder and the statistical properties of Josephson energy at the junction level, offering valuable insights for optimizing superconducting quantum processors. The established model provides a framework for predicting and mitigating the impact of interface roughness on qubit performance and scalability.

Josephson energy dependence on interface characteristics and statistical distribution is crucial for device performance

Researchers have developed a quantitative model to understand how interface roughness affects the Josephson energy within aluminium-based Josephson junctions. These junctions, crucial components in many quantum processors, exhibit performance variations due to even slight changes in their physical structure.

The model treats interface roughness as a Gaussian random field, defined by the root-mean-square roughness amplitude and the transverse correlation length, parameters informed by both existing experimental data and molecular dynamics simulations. Through numerical analysis of numerous junction samples, the study demonstrates that the Josephson energy follows a log-normal distribution, providing a statistically robust description of its variability.

The findings reveal that increasing the roughness amplitude elevates the mean Josephson energy, while a larger correlation length leads to a slight decrease. Importantly, the variance of the Josephson energy increases with both parameters, indicating a greater spread in possible values as roughness increases.

This work establishes a clear relationship between surface imperfections and junction performance, offering valuable insights for optimising junction design. The authors acknowledge that their model assumes independence between roughness parameters and identical roughness at both interfaces of the junction, areas requiring further experimental validation. Future research should focus on connecting this model to experimental characterisation of fabricated junctions and integrating it with computational microwave engineering tools to facilitate the co-design of junctions and their surrounding superconducting circuits.