A Simple and Scalable Method for Simulating Purcell Decay Channels in Transmon Qubits that is General across Linear Coupling Mechanisms

The ability to predict the decay rates of qubits and identify the physical origin of dissipation channels is critical to the design of performant quantum processing devices. We present a method for computing the loss rate of a qubit to multiple Purcell loss channels using a driven full wave electromagnetic simulation of the passive elements in a circuit under study. We build our method from a Langevin equation model of the qubit treated as a weakly anharmonic oscillator and write the coupling of the oscillator mode to the baths in terms of scattering parameters obtained from the simulation. In doing so we derive loss rates that are general across coupling mechanisms between the baths and the qubit. Furthermore, by lumping spectator qubits into the environment, this driven model allows for loss rates to be computed under various configurations of qubits frequencies after a single FEM simulation. This method is both scalable and shows excellent agreement with experiments on Purcell limited devices.