  The exact numerical solution of the nonlinear Ginzburg-Landau equation for
Josephson junctions is obtained, from which the nontrivial current density and
effective potential of the Josephson junction are accurately found. Tunneling
probabilities of the calculated bound states in the resulting potential well
are computed. The effects of junction and bias parameters such as thickness of
the insulating barrier, cross sectional area, bias current and magnetic field
are fully investigated using a successive perturbation approach. We define and
compute figures of merit for achieving optimal operation of phase qubits and
measurement of states. Particularly, it is predicted that Josephson junctions
with thicker barriers yield better performance in measurement of the phase
qubit. The proportion of other parameters is also studied and discussed for the
right situation of the setup. Results are in complete agreement with reported
experimental data.
