  We have developed an adiabatic Abelian geometric quantum computation strategy
based on the non-degenerate energy eigenstates in (but not limited to)
superconducting phase-qubit systems. The fidelity of the designed quantum gate
was evaluated in the presence of simulated thermal fluctuation in
superconducting phase qubits circuit and was found to be rather robust against
the random errors. In addition, it was elucidated that the Berry phase in the
designed adiabatic evolution may be detected directly via the quantum state
tomography developed for superconducting qubits.
