Simple, smooth and fast pulses for dispersive measurements in cavities and quantum networks

We demonstrate 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. For single-qubit measurements, current measurements are limited to the 99% fidelity range due to relaxation during the process. However, trying to go to shorter times to circumvent this with square or composite digital pulses leads to leftover cavity population after measurement of the same order of error. These effects can be suppressed using simple smooth pulse shapes from a similar family of pulses as DRAG shaping, used in the context of leakage removal in superconducting qubits; here, it can be derived exactly for arbitrarily many measured modes. Beyond single qubits, the measurement pulses are fully general to dispersive measurement systems. This includes multi-qubit and multi-state (leakage) measurements where the measurement can be done in a single shot and with a single homodyne phase. Another major challenge for fast measurement is depopulating Purcell filter cavities, which we show can readily be achieved using derivative shaping. Finally, we show how to apply the technique to cascaded cavity systems, e.g~for fast remote entanglement generation.