Open-Source Highly Parallel Electromagnetic Simulations for Superconducting Circuits

TL;DR

Open-source, HPC-enabled SQDMetal integrates Qiskit Metal, Gmsh, Palace, and ParaView to deliver a highly parallel workflow for designing and simulating superconducting quantum circuits. The paper validates accuracy via mesh-convergence benchmarks against COMSOL and Ansys, and demonstrates experimental agreement for resonators and transmon qubits, using EPR-based Hamiltonian extraction and inclusion of kinetic-inductance effects. The results show excellent agreement with commercial solvers in eigenmode and electrostatic simulations and reasonable alignment with experiments, while highlighting areas for improvement such as junction capacitance, kinetic inductance, and full 3D geometry. By unifying open-source tools in a notebook-driven pipeline, SQDMetal lowers barriers to entry and enables community-driven, scalable high-performance simulations for superconducting device design.

Abstract

Electromagnetic simulations form an indispensable part of the design and optimization process for superconducting quantum devices. Although several commercial platforms exist, open-source alternatives optimized for high-performance computing remain limited. To address this gap, we introduce SQDMetal, a Python-based API that integrates Qiskit Metal (IBM), Gmsh, Palace (AWS), and Paraview (Kitware) into an open-source, highly parallel simulation workflow for superconducting quantum circuits. SQDMetal enables accurate, efficient, and scalable simulations while remaining community-driven and free from commercial constraints. In this work, we validate SQDMetal through mesh convergence studies which benchmark SQDMetal against COMSOL Multiphysics and Ansys, demonstrating excellent agreement for both eigenmode and electrostatic (capacitance) simulations. Furthermore, we simulate superconducting resonators and transmon qubits, showing reasonable agreement with experimental measurements. SQDMetal also supports advanced capabilities, including Hamiltonian extraction via the energy participation ratio (EPR) method, incorporation of kinetic inductance effects, and full 3D modelling of device geometry for improved predictive accuracy. By unifying open-source tools into a single framework, SQDMetal lowers the barriers to entry for community members seeking to access high-performance simulations to assist in the design and optimization of their devices.

Figures (6)

• Figure 1: Visualization of the SQDMetal workflow and the software packages used for each process.
• Figure 2: Benchmark designs and associated eigenmode simulations. The simulations were performed using ANSYS, COMSOL and Palace. In each simulation, the mesh size (${\sim}{\text{DoF}}$) is decreased to converge to the continuum limit toward the LHS of the plots where $\text{DoF}\to\infty$. (a)-(b) A single CPW resonator with its mode $f_{\text{res}}$. (c)-(d) A CPW resonator with mode $f_{\text{res}}$ capacitively coupled to a feedline. (e)-(f) Transmon coupled to a CPW resonator with modes $f_{\text{qubit}}$ and $f_{\text{res}}$ respectively. (g)-(h) Two capacitively coupled transmons with modes $f_{\text{qubit L}}$ and $f_{\text{qubit R}}$ for the left and right qubits respectively. In all simulations $f_{\text{res}}$ refers to the fundamental resonator mode while $f_{\text{qubit}}$ refers to the qubit mode
• Figure 3: Capacitance matrix simulations of a transmon-resonator circuit. The design is from Fig. \ref{['fig:eig_results']}(e). The simulations were performed using ANSYS, COSMOL and Palace. In each simulation, the mesh size (${\sim}{\text{DoF}}$) was decreased to converge to the continuum limit on the LHS of the plot where $\text{DoF}\to\infty$. (a) Electrode labels for every contiguous metallic surface along with the (b) relevant entries to the capacitance matrix.
• Figure 4: Comparison of simulated and measured CPW resonator frequencies. The fundamental frequencies obtained from simulation and experiment for Al (aluminum), Nb (niobium), and Ta (tantalum) coplanar waveguide resonators are shown. Each point represents an individual resonator, with Al, Nb, and Ta denoted by blue, orange, and green circles, respectively. The dashed line indicates perfect agreement between simulated and measured values.
• Figure 5: Electric field visualization of the fundamental modes for each design. ParaView is used to visualize the results of the eigenmode simulation. (a) Single CPW resonator. (b) Single CPW resonator capacitively coupled to a feedline. (c) Transmon capacitively coupled to a CPW resonator with the top and bottom figures showing the transmon and resonator qubit modes. (d) Two capacitively coupled transmons with the top and bottom figures showing the left and right transmon modes.