Improving the accuracy of circuit quantization using the electromagnetic properties of superconductors

Abstract: Recent advances in quantum information processing with superconducting qubits have fueled a growing demand for scaling and miniaturizing circuit layouts. Despite significant progress, predicting the Hamiltonian of complex circuits remains a challenging task. Here, we propose an improved method for quantizing superconducting circuits that incorporates material- and geometry-dependent kinetic inductance. Our approach models superconducting films as reactive boundary elements, seamlessly integrating into the conventional circuit quantization framework without adding computational complexity. We experimentally validate our method using superconducting devices fabricated with 35 nm-thick disordered niobium films, demonstrating significantly improved accuracy in predicting the Hamiltonian based solely on the device layout and material properties of superconducting films and Josephson junctions. Specifically, conventional methods exhibit an average error of 5.4% in mode frequencies, while our method reduces it to 1.1%. Our method enables systematic studies of superconducting devices with disordered films or compact elements, facilitating precise engineering of superconducting circuits at scale.