  We present a new readout method for a superconducting flux qubit, based on
the measurement of the Josephson inductance of a superconducting quantum
interference device that is inductively coupled to the qubit. The intrinsic
flux detection efficiency and back-action are suitable for a fast and
nondestructive determination of the quantum state of the qubit, as needed for
readout of multiple qubits in a quantum computer. We performed spectroscopy of
a flux qubit and we measured relaxation times of the order of 80 $\mu s$.
