Quantum nondemolition measurement of a superconducting qubit in the weakly projective regime.

Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong backaction. We show that the backaction of a dc-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum nondemolition character, with a QND fidelity of 75%.