  Non-Markovian noise can be a significant source of errors in superconducting
qubits. We develop gate sequences utilising mirrored pseudoidentities that
allow us to characterise and model the effects of non-Markovian noise on both
idle and driven qubits. We compare three approaches to modelling the observed
noise: (i) a Markovian noise model, (ii) a model including interactions with a
two-level system (TLS), (iii) a model utilising the post Markovian master
equation (PMME), which we show to be equivalent to the qubit-TLS model in
certain regimes. When running our noise characterisation circuits on a
superconducting qubit device we find that purely Markovian noise models cannot
reproduce the experimental data. Our model based on a qubit-TLS interaction, on
the other hand, is able to closely capture the observed experimental behaviour
for both idle and driven qubits. We investigate the stability of the noise
properties of the hardware over time, and find that the parameter governing the
qubit-TLS interaction strength fluctuates significantly even over short
time-scales of a few minutes. Finally, we evaluate the changes in the noise
parameters when increasing the qubit drive pulse amplitude. We find that
although the hardware noise parameters fluctuate significantly over different
days, their drive pulse induced relative variation is rather well defined
within computed uncertainties: both the phase error and the qubit-TLS
interaction strength change significantly with the pulse strength, with the
phase error changing quadratically with the amplitude of the applied pulse.
Since our noise model can closely describe the behaviour of idle and driven
qubits, it is ideally suited to be used in the development of quantum error
mitigation and correction methods.
