Optimize Purcell filter design for reducing influence of fabrication variation

To protect superconducting qubits and enable rapid readout, optimally designed Purcell filters are essential. To suppress the off-resonant driving of untargeted readout resonators, individual Purcell filters are used for each readout resonator. However, achieving consistent frequency between a readout resonator and a Purcell filter is a significant challenge. A systematic computational analysis is conducted to investigate how fabrication variation affects filter performance, through focusing on the coupling capacitor structure and coplanar waveguide (CPW) transmission line specifications. The results indicate that the T-type enclosing capacitor (EC), which exhibits lower structural sensitivity, is more advantageous for achieving target capacitance than the C-type EC and the interdigital capacitor (IDC). By utilizing a large-sized CPW with the T-type EC structure, fluctuations in the effective coupling strength can be reduced to 10%, given typical micro-nanofabrication variances. The numerical simulations presented in this work minimize the influence of fabrication deviations, thereby significantly improving the reliability of Purcell filter designs.