Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong back-action. We show that the back-action 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 non-demolition character, with a QND fidelity of 75 %.
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