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Nested Uhrig dynamical decoupling (NUDD) is a highly efficient quantum errorsuppression scheme that builds on optimized single axis UDD sequences. We provethe universality of NUDD and analyze its suppression of different error typesin the setting of generalized control pulses. We present an explicit lowerbound for the decoupling order of each error type, which we relate to thesequence orders of the nested UDD layers. We find that the error suppressioncapabilities of NUDD are strongly dependent on the parities and relativemagnitudes of all nested UDD sequence orders. This allows us to predict theoptimal arrangement of sequence orders. We test and confirm our analysis usingnumerical simulations.

Universality proof and analysis of generalized nested Uhrig dynamical decoupling