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We propose a superconducting phase qubit on the basis of the radio-frequencySQUID with the screening parameter value $\beta_L = (2\pi/\Phi_0)LI_c \approx1$, biased by a half flux quantum $\Phi_e=\Phi_0/2$. Significant anharmonicity($> 30%$) can be achieved in this system due to the interplay of the cosineJosephson potential and the parabolic magnetic-energy potential that ultimatelyleads to the quartic polynomial shape of the well. The two lowest eigenstatesin this global minimum perfectly suit for the qubit which is insensitive to thecharge variable, biased in the optimal point and allows an efficient dispersivereadout. Moreover, the transition frequency in this qubit can be tuned withinan appreciable range allowing variable qubit-qubit coupling.

Superconducting phase qubit based on the Josephson oscillator with strong anharmonicity