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arXiv:2511.09041

Electromagnetic Feature Extraction in Superconducting Quantum Circuits: An Open-Source Finite-Element Workflow Using Palace

Jiale Ye, Jiaheng Wang, Yu-xi Liu

quant-phSubmitted Nov 12, 2025• Announced Nov 13, 2025• 0 citations
arXivHTMLPDF

Abstract

Accurate electromagnetic (EM) feature extraction, including element characterization, eigenmodes, and field distributions, is essential for superconducting quantum circuit design. To streamline this process, we present a workflow built around Palace, an open-source, high-performance finite element method solver tailored for quantum applications. Starting from circuit layouts, the workflow automates mesh generation, multiple EM solver processing, and EM-to-Hamiltonian post-processing. We benchmark the workflow on a chip with bare resonators and qubits coupled with readout resonators, achieving resonator frequencies prediction within 0.3% and 3 out of 4 external couplings within 16% of cryogenic measurements. These results demonstrate open-source EM tools can match commercial accuracy while offering scalable, license-free analysis. Our Palace-based workflow provides an accessible and extensible foundation for rapid superconducting circuit development and materials-loss studies.

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Accurate electromagnetic (EM) feature extraction, including element characterization, eigenmodes, and field distributions, is essential for superconducting quantum circuit design. To streamline this process, we present a workflow built around Palace, an open-source, high-performance finite element method solver tailored for quantum applications. Starting from circuit layouts, the workflow automates mesh generation, multiple EM solver processing, and EM-to-Hamiltonian post-processing. We benchmark the workflow on a chip with bare resonators and qubits coupled with readout resonators, achieving resonator frequencies prediction within 0.3% and 3 out of 4 external couplings within 16% of cryogenic measurements. These results demonstrate open-source EM tools can match commercial accuracy while offering scalable, license-free analysis. Our Palace-based workflow provides an accessible and extensible foundation for rapid superconducting circuit development and materials-loss studies.
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.
Accurate prediction of qubit–qubit exchange coupling is essential for superconducting processor design. We present and benchmark an automated full-wave electromagnetic (EM) workflow in Keysight Advanced Design System (ADS) and QuantumPro that evaluates pairwise exchange couplings from layout-level multiport responses using the established transfer-impedance relation of Solgun et al. Because many scalable superconducting processors employ repeated or near-repeated coupling motifs, reduced EM models can lower computational cost if their error is quantified. We study nearest-neighbor couplings in a reconstructed geometry based on the IBM Q 16 Rueschlikon processor using a sixteen-qubit (16Q) coupling-network model, four-qubit (4Q) unit-cell models, and pair-specific two-qubit (2Q) sub-blocks. The 4Q models provide a like-for-like external benchmark because they match the model extent used by Solgun et al. for the published full-wave coupling calculations. The 4Q models reproduce the published simulated couplings with a 3.70% mean absolute percentage error and differ from 16Q by 3.62% on average. For the representative single solves reported here, the 16Q solve takes approximately 7.2 times as long as 4Q and requires 5.7 times the peak memory. This supports 4Q as a practical reduced model for quantitative local coupling prediction. Further reduction to 2Q changes the couplings by 6.17% on average but remains effective for inexpensive mesh-convergence screening. The resulting workflow provides automated exchange-coupling extraction together with model-extent and convergence assessment in a commercial microwave EDA environment.
High-fidelity control of superconducting quantum processors requires accurate characterization of electromagnetic coupling strengths among the device's constituent elements. Accurately extracting these couplings across large-scale architectures, presently featuring hundreds of qubits, poses a challenging multi-scale modeling problem. This requires resolving scales from the nanometer-scale geometry of Josephson junctions and their leads to the centimeter-scale size of the enclosing metallic packages. We present four numerical coupling extraction methods based on the avoided level crossing, the energy participation ratio, the induced electromotive force, and the impedance matrix. These methods are tailored to work with commercially available 3D electromagnetic solvers. We benchmark these techniques on a 10×1010\times1010×10 array of transmon qubits, extracting their couplings to standing package modes. Our results show that these methods yield consistent coupling strengths with a maximum relative difference of less than 5%.
We present an open-source database of superconducting quantum device designs that may be used as the starting point for customized devices. Each design can be generated programmatically using the open-source Qiskit Metal package, and simulated using finite-element electromagnetic solvers. We present a robust workflow for achieving high accuracy on design simulations. Many designs in the database are experimentally validated, showing excellent agreement between simulated and measured parameters. Our database includes a front-end interface that allows users to generate ``best-guess'' designs based on desired circuit parameters. This project lowers the barrier to entry for research groups seeking to make a new class of devices by providing them a well-characterized starting point from which to refine their designs.
An accurate and efficient numerical electromagnetic model for superconducting qubits is essential for characterizing and minimizing design-dependent dielectric losses. The energy participation ratio (EPR) is the commonly adopted metric used to evaluate these losses, but its calculation presents a severe multiscale computational challenge. Conventional finite element method (FEM) requires 3D volumetric meshing, leading to prohibitive computational costs and memory requirements when attempting to capture singular electric fields at nanometer-thin material interfaces. To address this bottleneck, we propose SesQ, a surface integral equation simulator tailored for the precise simulation of the EPR. By applying discretization on 2D surfaces, deriving a semi-analytical multilayer Green's function, and employing a dedicated non-conformal boundary mesh refinement scheme, SesQ accurately resolves singular edge fields without an explosive growth in the number of unknowns. Validations with analytically solvable models demonstrate that SesQ accelerates capacitance extraction by roughly two orders of magnitude compared to commercial FEM tools. While achieving comparable accuracy for capacitance extraction, SesQ delivers superior precision for EPR calculation. Simulations of practical transmon qubits further reveal that FEM approaches tend to significantly underestimate the EPR. Finally, the high efficiency of SesQ enables rapid iteration in the layout optimization, as demonstrated by minimizing the EPR of the qubit pattern, establishing the simulator as a powerful tool for the automated design of low-loss superconducting quantum circuits.
Translating superconducting quantum chip layouts into physically meaningful simulation records is a critical step in quantum hardware development, yet current datasets rarely capture the electromagnetic (EM) effects involved in this process. We propose SQChip-EM, an open layout to EM simulation dataset based on Qiskit Metal that links parameterized layout designs to Ansys HFSS and Q3D simulation results. Unlike abstract circuit datasets, SQChip-EM preserves layout dependent EM evidence through GDSII files, raw simulation outputs, and JSON annotations covering frequencies, anharmonicity, dispersive shifts, and coupling parameters. These annotations form reusable simulation level ''virtual chip'' records for downstream workflows such as initialization, calibration tuning, and control simulation. SQChip-EM also includes three illustrative benchmark tasks, including design to metric regression, specification feasibility classification, and inverse design retrieval, together with one downstream workflow use case. By releasing data, code, and evaluation protocols, SQChip-EM provides a standardized data resource for ML assisted quantum electronic design automation.