  We study a readout scheme of superconducting flux qubit state with a Cooper
pair box as a transmon. The qubit states consist of the superpositions of two
degenerate states where the charge and phase degrees of freedom are entangled.
Owing to the robustness of transmon against external fluctuations, our readout
scheme enables the quantum non-demolition and single-shot measurement of flux
qubit states. The qubit state readout can be performed by using the non-linear
Josephson amplifiers after a $\pi/2$-rotation driven by an ac-electric field.
