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The exact numerical solution of the nonlinear Ginzburg-Landau equation forJosephson junctions is obtained, from which the nontrivial current density andeffective potential of the Josephson junction are accurately found. Tunnelingprobabilities of the calculated bound states in the resulting potential wellare computed. The effects of junction and bias parameters such as thickness ofthe insulating barrier, cross sectional area, bias current and magnetic fieldare fully investigated using a successive perturbation approach. We define andcompute figures of merit for achieving optimal operation of phase qubits andmeasurement of states. Particularly, it is predicted that Josephson junctionswith thicker barriers yield better performance in measurement of the phasequbit. The proportion of other parameters is also studied and discussed for theright situation of the setup. Results are in complete agreement with reportedexperimental data.

Optimization of Junction and Bias Parameters in readout of Phase Qubit