A Geometrical Approach To Robust Quantum Control That Respects Pulse Constraints And Minimizes Gate Times

We extend our recently introduced geometrical method for designing driving fields that suppress quasistatic noise errors while performing single-qubit operations to incorporate realistic experimental constraints on the pulse shapes. We show that this approach can be made compatible with experimental restrictions on the pulse amplitude or rise time without sacrificing any of the robustness to noise. By leveraging the generality of our geometrical approach, we perform a variational analysis to derive the globally optimal driving pulse that obeys a given set of pulse shape constraints while minimizing the operation time and while cancelling noise errors to second order. In cases where the optimal pulses are not smooth, we provide a method based on our geometrical approach to obtain experimentally feasible smooth pulses that closely approximate the optimal ones without sacrificing the fidelity. We present systematic comparisons between our pulses and standard error-correcting pulse sequences to highlight the benefits of building experimental waveform constraints into dynamically corrected gate designs.