  An adiabatic method for a single-shot non-demolition measurement of the phase
qubit is suggested. The qubit is inductively coupled to a low-frequency
resonator, which in turn is connected with a classical measurement device
(phase meter). The resonator drives adiabatic oscillations of the supercurrent
in the qubit loop. The back reaction of the qubit loop on the resonator depends
on the qubit state. Measuring the phase shift of the resonator's oscillations
one can determine the state of the qubit. Numerical computations with available
experimental parameters show that the phase difference between the two qubit
states increases at a rate of 0.0044 rad/ns with the fidelity of about 0.9989
and the measurement time of about 100 ns. The fidelity of the measurement is
estimated taking into consideration possible quantum transitions inside and
outside the qubit manifold. An increase of the phase difference is possible but
it is linked to a reduction of the fidelity. The requirements for the
reproducibility of the qubit and resonator parameters are formulated.
