Rapid ballistic readout for flux qubits

We suggest a magnetic flux detector that can be optimized with respect to the measurement back action, e.g., for the situation of quantum measurements. The detector is based on manipulation of ballistic motion of individual fluxons in a Josephson transmission line (JTL), with the output information contained in either probabilities of fluxon transmission and reflection, or time delay associated with the fluxon propagation through the JTL. We calculate the detector characteristics of the JTL and derive equations for conditional evolution of the measured system both in the transmission and reflection and the time-delay regimes. Combination of the quantum-limited detection with control over individual fluxons should make the JTL detector suitable for implementation of nontrivial quantum measurement strategies, including conditional measurements and feedback control schemes.