  Berry's phase often appears in quantum two-level systems with a degeneracy.
An example of such a system is a spin-1/2 particle in a magnetic field. As the
magnetic field is slowly evolved through a closed path, the particle has been
shown to acquire an additional phase called Berry's phase, in addition to the
usual dynamical phase. This phase has been found in two-level quantum systems
intrinsic to many superconducting qubits and has particularly been calculated
for the charge, flux and Josephson phase qubit. Here, we present an alternative
derivation of the Berry's phase in a current-biased Josephson junction qubit.
We also calculate the complete Berry's phase evaluated over a closed loop in a
frequency parameter space and compare this with the geometric phase. From this
comparison, we examine the possibility of using a single phase qubit for
topological quantum computing.
