Spontaneous Emission Rate Modeling of Transmon Qubits

Transmon qubits are one of the leading candidates being pursued to achieve various forms of quantum computation. These qubits consist of superconducting Josephson junctions that are embedded in planar microwave circuitry, such as coplanar waveguides. Generally, the transmon qubit will be coupled to a number of microwave resonators in order to control the qubit, read out its state, and drive qubit-qubit interactions. This requires a careful balance between providing control of the qubit and protecting its fragile quantum state. One of the primary mechanisms that can destroy the qubit's state is by spontaneously emitting its excitation into the many microwave transmission lines around the qubit. Hence, modeling the spontaneous emission rate for practical qubit implementations can provide valuable information about the performance limitations of a device before fabrication. 

However, the commonly used theoretical models for analyzing transmon qubits are not conducive to rigorously determining the spontaneous emission rate of practical devices. We have addressed this problem by developing a more general theoretical model for the interaction of a transmon qubit with electromagnetic fields. With this generalized model, we can show that the spontaneous emission rate of the transmon qubit can be computed using completely classical full-wave computational electromagnetics methods. We have validated this approach by analyzing different superconducting circuit quantum devices. Our results show good agreement with the measured spontaneous emission rates of devices fabricated with similar parameters to our numerical models.

(a) Device layout of a single photon source with the transmon qubit located near the "input" of the device. (b) Equivalent transmission line model from the perspective of the transmon qubit, where Yeq denotes the admittance needed to compute the spontaneous emission rate using simplified theoretical approaches. (c) Relaxation time (inverse of spontaneous emission rate) of the transmon for various qubit locations computed using our full-wave approach and the best-fit transmission line model. The other qubit locations that simulations were performed at are denoted in (a).

(a) Transmon device with a "Purcell filter" designed to lower the spontaneous emission rate of the qubit while still allowing for quick measurement and control to occur. (b) Relaxation time of the transmon computed using our full-wave approach and a best-fit transmission line model. The transmission line model without a Purcell filter included is also shown to highlight the drop in spontaneous emission rate that the Purcell filter provides.