Optimal pulse shaping for dispersive readout

Quantum non-demolition measurement is essential for quantum error correction. In superconducting qubits, measurement is enacted by dispersively scattering microwaves off the qubit through a readout resonator. This measurement must be completed quickly to prevent qubit decay errors, and with low power to avoid undesired measurement-induced transitions. These requirements are in direct conflict, since the achievable signal-to-noise ratio increases with both the readout power and the duration. In this talk, we demonstrate a method to design readout pulses that minimize the readout power and duration. To prevent residual dephasing, our pulses leave the readout resonator empty after the measurement, even in the presence of the resonator's Kerr nonlinearity. Our method is simple and computationally efficient, circumventing the necessity to perform costly master equation simulations. The pulses that we find are analytically optimal when the rate of unwanted measurement transitions scales linearly with power.