Fast dispersive, Purcell-filtered measurement and reset using smooth and simple analytic pulse shapes

We present a dispersive, measurement pulse shaping technique that allows for arbitrarily fast quantum non-demolition, single-quadrature measurements of non-linear systems and unconditionally leaves the measurement resonator empty. Leftover cavity population from short measurements with square or composite digital pulses can be suppressed using instead simple smooth pulse shapes from an analogous family of DRAG shapes; here, it can be derived exactly for arbitrarily many measured modes. The results are easily generalizable, including single-shot, single-quadrature, measurements of multi-qubit and multi-state (leakage) systems. One can also straightorwardly incorporate Purcell filter cavities, which can be depopulated simultaneously via the same technique. Finally, we show how to apply the technique to cascaded cavity networks, e.g. for fast remote entanglement generation, or in non-dispersive single-photon networks, and discuss applicability to singe flux quantum (SFQ) readout.