Decoupling a spin qubit from high-frequency Larmor dynamics of a GaAs nuclear spin bath*

We present a technique of decoupling a spin qubit in a GaAs/AlGaAs heterostructure from low- and high-frequency noise arising from hyperfine interaction of electrons with nuclear spins. We use Carr-Purcell-Meiboom-Gill sequences in which we synchronize the repetition rate of $\pi$ pulses to difference Larmor frequencies of $^{69}$Ga, $^{71}$Ga and $^{75}$As nuclei. This decouples the qubit both from low-frequency noise due to diffusion of nuclear spins and from noise at selected high frequencies, allowing us to apply more than a thousand $\pi$ pulses in a sequence. We demonstrate a coherence time of a singlet-triplet qubit of 0.87 ms, i.e. five orders of magnitude longer than the inhomogeneous dephasing time intrinsic to GaAs.