Current simulation and inductance extraction for multilayer superconducting circuits with a posteriori and semi a priori adaptive mesh refinement

Abstract Superconducting circuit development represents a critical area of research in superconductivity, offering significant potential for applications in artificial intelligence and quantum computing. In the design of such circuits, inductance plays a pivotal role, second only to the Josephson junction in importance. As superconducting circuit designs grow increasingly complex, there is a pressing need for efficient and accurate inductance extraction methods. The two primary approaches for this purpose are the volume electric current integral equation and the London equation. While the London equation offers several advantages, its relatively high computational cost and lack of direct compatibility with analog simulation tools have hindered its widespread adoption in superconducting circuit design. To overcome these limitations, we developed a finite element solver for the London equation incorporating both a posteriori and semi a priori error estimators. Our adaptive solver can refine the mesh based on current density, thereby drastically improving computational efficiency. Numerical experiments indicate that the proposed method can reduce the computational time from 39.05% to 84.89% compared to a uniform mesh. Additionally, we introduce an improved inductance extraction method, facilitating seamless integration of the London equation model with analog simulation tools such as JoSIM. The efficacy of our approach is validated through numerical simulations on a testbench comprising multiple advanced ColdFlux circuits, achieving superior accuracy compared to uniform mesh methods. To the best of our knowledge, both our methodology and its application to such sophisticated circuits have not been previously reported. These advancements provide a valuable foundation for next-generation superconducting circuit design and the broader development of superconducting computing technologies.