Filter functions for robust quantum control

Correlated noise such as the 1/f noise found in many solid-state systems limits the improvement of gate fidelities in quantum information processors because it is unfeasibly expensive to simulate using conventional methods. This issue is exacerbated when considering algorithms in the presence of noise with correlation times larger than gate durations as gate errors may interfer. Previously, we have shown how filter functions can be used to compute the effect of such noise on gate sequences. Here, I will show how the effect can be efficiently mitigated in gradient-based robust quantum control by introducing analytical results for the derivatives of filter functions. Filter functions represent a spectrally resolved susceptibility to external perturbations and allow for computing complete quantum processes and hence also gate fidelities or leakage rates. Using the analytical expressions for the gradients, we can efficiently optimize control pulses for high-fidelity gates. As an example, I show how one can obtain Rabi pulses that are robust against 1/f noise. I conclude by presenting the open-source filter_functions software framework (https://github.com/qutech/filter_functions), which facilitates computing filter functions and their derivatives for arbitrary quantum gates.