  We describe temporally correlated noise processes that influence the idle
evolution of a superconducting transmon qubit. To model the composite
qubit-environment system we use quantum circuit theory, and we show how a
circuit Hamiltonian can be derived for transverse noise affecting the qubit.
Based on the time-convolutionless projection operator method, we construct a
time-local master equation which, when transformed to its canonical Lindblad
form, exhbitis a decay rate that is negative at all times, corresponding to
eternally non-Markovian dynamics. By expressing the solution of the master
equation in the Kraus representation, we identify two crucial non-Markovian
phenomena: periodic revivals of coherence, and the appearance of additional
frequencies far from the qubit frequency in the precession of the qubit state.
When a single qubit gate acts on the qubit state, these extra frequency terms
rotate undesirably and they effectively act as the memory of the state prior to
the rotation around the Bloch sphere.
