  We present a quantum open-system approach to analyze the nonunitary dynamics
of a superconducting qubit when it evolves under the influence of external
noise. We consider the presence of longitudinal and transverse environmental
fluctuations affecting the system's dynamics and model these fluctuations by
defining their correlation function in time. By using a Gaussian-like noise
correlation, we can study low- and high-frequency noise contribution to
decoherence and implement our results in the computation of geometric phases in
open quantum systems. We numerically study when the accumulated phase of a
solid-state qubit can still be found close to the unitary (Berry) one. Our
results can be used to explain experimental measurements of the Berry phase
under high-frequency fluctuations and design experimental future setups when
manipulating superconducting qubits.
