Frequency-domain pulse engineering for fast qubit readout and resonator reset

The state of a superconducting qubit is typically determined by measuring the dispersive shift χ of a superconducting resonator with coupling rate κ to a transmission line. Large χ/κ ratio is beneficial for high-fidelity readout. While small κ protects the qubit from the noisy environment, it has the big disadvantage of limiting the speed of measurement. In particular, photons linger in the resonator for a time of several 1/κ, causing decoherence of the qubit and blocking subsequent measurement. Here we present a microwave pulse scheme which, regardless of the state of the qubit, populates the readout resonator, measures the state of the qubit, and empties the resonator, all in a time much faster than 1/κ. The pulse is designed in the frequency domain by shaping its spectral content at the dressed-resonance frequencies. The pulse envelope is derived through inverse Fourier transform, rather than relying on brute-force numerical optimization. We evaluate the performance of the pulse scheme in different regimes of χ/κ through both simulation and experiment, and we comment on the theoretically achievable single-shot fidelity of the method.