In superconducting quantum processors, the predictability of device parameters is of increasing importance as many labs scale up their systems to larger sizes in a 3D-integrated architecture. In particular, the properties of superconducting resonators must be controlled well to ensure high-fidelity multiplexed readout of qubits. Here we present a method, based on conformal mapping techniques, to predict a resonator's parameters directly from its 2D cross-section, without computationally heavy and time-consuming 3D simulation. We demonstrate the method's validity by comparing the calculated resonator frequency and coupling quality factor with those obtained through 3D finite-element-method simulation and by measurement of 15 resonators in a flip-chip-integrated architecture. We achieve a discrepancy of less than 2% between designed and measured frequencies, for 6-GHz resonators. We also propose a design method that reduces the sensitivity of the resonant frequency to variations in the inter-chip spacing.
@article{arxiv.2305.05502,
title = {Experimentally verified, fast analytic and numerical design of superconducting resonators in flip-chip architectures},
author = {Hang-Xi Li and Daryoush Shiri and Sandoko Kosen and Marcus Rommel and Lert Chayanun and Andreas Nylander and Robert Rehammar and Giovanna Tancredi and Marco Caputo and Kestutis Grigoras and Leif Grönberg and Joonas Govenius and Jonas Bylander},
journal= {arXiv preprint arXiv:2305.05502},
year = {2023}
}