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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 themagnetic field is slowly evolved through a closed path, the particle has beenshown to acquire an additional phase called Berry's phase, in addition to theusual dynamical phase. This phase has been found in two-level quantum systemsintrinsic to many superconducting qubits and has particularly been calculatedfor the charge, flux and Josephson phase qubit. Here, we present an alternativederivation 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 afrequency parameter space and compare this with the geometric phase. From thiscomparison, we examine the possibility of using a single phase qubit fortopological quantum computing.

Berry's phase in the Josephson phase qubit