Ideal Quantum non-demolishing measurement of a flux qubit at variable bias

We propose a scheme to realize a quantum non-demolition (QND) measurement of a superconducting flux qubit by a Josephson bifurcation amplifier. Our scheme can implement a perfect QND measurement for a qubit subject to a variable magnetic bias. Measurement back-action induced qubit relaxation can be suppressed and hence the QND fidelity is expected to be high over a wide range of bias conditions.