Noise filtering of composite pulses for singlet-triplet qubits*

Dynamically corrected gates are useful measures to combat decoherence in spin qubit systems. They are, however, mostly designed assuming the static-noise model and may thus be considered low-frequency noise filters. In this talk we carefully examine the applicability of a particular type of dynamically corrected gates, namely the \textsc{supcode} designed for singlet-triplet qubits, under realistic $1/f^\alpha$ noises. Through randomized benchmarking, we have found that \textsc{supcode} offers improvement of the gate fidelity for $\alpha>1$ and the improvement becomes exponentially more pronounced with the increase of the noise exponent $\alpha$ up to 3. On the other hand, for small $\alpha$ \textsc{supcode} will not offer any improvement. We also present the computed filter transfer functions for the \textsc{supcode} gates for nuclear and charge noise respectively and have found that they are consistent with the finding from the benchmarking.