Keyldysh assisted evaluation of decoherence errors in driven qubits*

Decoherence errors have been a bottleneck in realizing high-fidelity qubit operations. Such errors are usually modeled using the Lindblad master equation. However, when correlated noise (both classical and quantum) is present and when the qubit is driven by a short pulse, the Lindblad master equation is not sufficiently accurate. To overcome this obstacle, we develop a more accurate estimation tool based on the Keldysh expansion. After suitable approximation, this yields a completely positive and trace preserving (CPTP) map of the qubit density matrix. We further show how this tool catches the influence of qubit driving in the presence of classical and quantum noise. This advanced technique can be integrated with gradient ascent pulse engineering, which can be used to mitigate decoherence errors during gate operations.