  We present a readout method for superconducting flux qubits. The qubit
quantum flux state can be measured by determining the Josephson inductance of
an inductively coupled DC superconducting quantum interference device
(DC-SQUID). We determine the response function of the DC-SQUID and its
back-action on the qubit during measurement. Due to driving, the qubit energy
relaxation rate depends on the spectral density of the measurement circuit
noise at sum and difference frequencies of the qubit Larmor frequency and SQUID
driving frequency. The qubit dephasing rate is proportional to the spectral
density of circuit noise at the SQUID driving frequency. These features of the
backaction are qualitatively different from the case when the SQUID is used in
the usual switching mode. For a particular type of readout circuit with
feasible parameters we find that single shot readout of a superconducting flux
qubit is possible.
