Understanding and Mitigating Loss in Transmon Qubits Due to Flux Line Coupling

In a tunable transmon, the qubit frequency can be adjusted by varying the external flux that passes through the SQUID loop. In multi-qubit devices, it is typically necessary to deliver the external flux through local flux lines that run close to each qubit. However, the flux line provides an additional channel for energy loss, thereby reducing the qubit lifetime (T1). This undesired loss mechanism is often referred to as the M’ (“M prime”) coupling [1, 2], to distinguish it from the mutual inductance M that describes the desired coupling between the external bias current and the flux threading the SQUID loop.

In this work, we study this parasitic M’ coupling mechanism between a qubit and its local flux line. We present a theoretical model of a tunable transmon and analytically calculate the loss incurred due to a local flux line. We simulate practical qubit devices to obtain agreement with the theoretical model and provide recommendations for how to best assess the performance of a flux line over the full range of possible external flux biases. Finally, we compare our theoretical model to measured devices. This work provides an optimization strategy for local flux line design across a range of superconducting circuit devices.