Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences

treatment of bath operators by considering two limiting cases for the coupling strengths of system-bath and pure-bath, namely: (i) J < β and (ii) β ≪ J [recall Eq. (18)]. In case (i), the coupling to the environment induces slow dynamics while the environment itself has fast dynamics. In case (ii), the coupling to the environment is fast but relatively stable due to the environment’s slow internal dynamics. This regularity makes case (ii) especially attractive for dynamical decoupling, or similar methods [27], while case (i) is a worst case scenario. Both these cases are still within the convergence domain of Magnus expansion (‖He‖T < 1, see subsection III B). Outside the convergence domain (e.g. corresponding to long experiment duration), deterministic decoupling might be replaced by randomized decoupling methods, for which there is some evidence of better performance [12]. In practice the co-existence of various bath regimes makes hybrid decoupling methods a practical choice for long-time decoupling [13].