  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.
