Fast analytic and numerical design of superconducting resonators in flip-chip architectures

  1. Hang-Xi Li,
  2. Daryoush Shiri,
  3. Sandoko Kosen,
  4. Marcus Rommel,
  5. Lert Chayanun,
  6. Andreas Nylander,
  7. Robert Rehammer,
  8. Giovanna Tancredi,
  9. Marco Caputo,
  10. Kestutis Grigoras,
  11. Leif Grönberg,
  12. Joonas Govenius,
  13. and Jonas Bylander
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 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.