Concatenated dynamical decoupling in a solid-state spin bath

Concatenated dynamical decoupling (CDD) pulse sequences hold much promise as a strategy to mitigate decoherence in quantum information processing. It is important to investigate the actual performance of these dynamical decoupling strategies in real systems that are promising qubit candidates. In this Rapid Communication, we compute the echo decay of concatenations of the Hahn echo sequence for a solid-state electronic spin qubit in a nuclear spin bath using a cluster expansion technique. We find that each level of concatenation reverses the effect of successive levels of intrabath fluctuations. On the one hand, this advances CDD as a versatile and realistic decoupling strategy. On the other hand, this invalidates, as overly optimistic, results of the simple pair approximation used previously to study restoration, through CDD, of coherence lost to a mesoscopic spin bath.