Aspects of FEM modeling of quantum devices and construction of their loss budget

Further improvements of relaxation times of transmon qubits require calculations of the loss budget that details individual contributions of various elements constituting a quantum device such as amorphous surface oxides, substrate, metal-air and metal-substrate interfaces, etc. into the combined relaxation times. Such accounting is impossible without detailed picture of the EM field distribution and participation ratios. While simplified scheme capturing only the general geometric shape of a devices provides good starting point for calculation of such parameters as transition frequency, anharmonicity, and coupling to other devices on a chip, loss budget calculations require finer resolved model that accounting for thicknesses of metallization layers, surface oxides, and behavior of EM fields around sharp corners and edges. This is especially relevant for the qubits fabricated using newly developed techniques that use encapsulation, undercut, etc.

We discuss relevant details of numerical model construction and calculations as well as the most critical geometric features of transmon qubits and CPW resonators.