# Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem

## TL;DR

This paper investigates how microwave drive power affects relaxation rates in superconducting qubits, revealing that non-conserving terms in the Josephson potential can significantly influence relaxation, impacting measurement fidelity.

## Contribution

It introduces a perturbative expansion method to derive effective master equations accounting for drive-dependent relaxation in weakly anharmonic qubits, highlighting the role of non-conserving terms.

## Key findings

- Number non-conserving terms cause significant drive-power dependence of relaxation rates.
- Effective master equations with renormalized parameters accurately describe drive-dependent relaxation.
- The method is broadly applicable to driven-dissipative quantum systems with weak non-linearity.

## Abstract

Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number non-conserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e. Kerr interactions) shows that number non-conserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly non-linear degrees of freedom.