We introduce a detection scheme for the state of a qubit, which is based on
resonant few-photon transitions in a driven nonlinear resonator. The latter is
parametrically coupled to the qubit and is used as its detector. Close to the
fundamental resonator frequency, the nonlinear resonator shows sharp resonant
few-photon transitions. Depending on the qubit state, these few-photon
resonances are shifted to different driving frequencies. We show that this
detection scheme offers the advantage of small back action, a large
discrimination power with an enhanced read-out fidelity, and a sufficiently
large measurement efficiency. A realization of this scheme in the form of a
persistent current qubit inductively coupled to a driven SQUID detector in its
nonlinear regime is discussed.Comment: 10 pages, 6 figures. To appear in Phys. Rev.
