Fast and Accurate Design of Readout Resonators for Flip-Chip-Integrated Multi-Qubit Superconducting Quantum Processors

Predicting the parameters of superconducting resonators is important for achieving high qubit readout fidelity and preventing substantial Purcell decay. We use analytic equations, derived from conformal mapping, and 2D cross-sectional EM simulation, to calculate the frequency and coupling quality factor of resonators within a flip-chip geometry. We achieve a good agreement between this method and the more resource-intensive 3D FEM simulation under different inter-chip distances, considering the effective length due to the resonator-qubit coupling structure. Our method dramatically reduces the simulation time required for a multi-qubit quantum processor chip. We measured the inter-chip distance after flip-chip bonding to infer the resonators' capacitance and inductance. We show that the calculated resonator frequencies deviate from the measured values by less than 2%.