Deriving effective coupling strength via Born-Oppenheimer approximation for superconducting qubits

The development of high-fidelity quantum gates is paramount to the scalability of quantum processors. Tunable couplers have played a key role in the realization of these low error rate quantum gates in superconducting circuits. The derivation of the effective coupling strength between the qubits is usually enabled by a Schrieffer-Wolff transformation. We propose a simpler method of obtaining this effective coupling using an approach similar to the Born-Oppenheimer approximation and, finally, formally justify our method.