Systematic Perturbation Theory for Frequency and Lifetime Renormalization of Superconducting Qubits*

We introduce two quantitatively consistent methods for perturbatively calculating the renormalization of both frequency and relaxation time for transmon-type superconducting qubits, relevant to recent experiments [1]. We consider a general situation where the qubit is embedded in an open linear electromagnetic environment, whose properties are determined by its Maxwell Green's function [2]. The two calculation strategies provide systematic corrections to the system poles to arbitrary order and are not limited by Hilbert space truncation.

[1] S. Mundhada, S. Shankar, A. Narla, E. Zalys-Geller, S. M. Girvin, and M. Devoret in APS Meething Abstract (2016).
[2] M. Malekakhlagh, A. Petrescu, and H. E. Tureci, Phys. Rev. A 94, 063848 (2016).