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The impact of control sequences on the environmental coupling of a quantumsystem can be described in terms of a filter. Here we analyze how the coherentevolution of two interacting spins subject to periodic control pulses, at theexample of a nitrogen vacancy center coupled to a nuclear spin, can bedescribed in the filter framework in both the weak and the strong couplinglimit. A universal functional dependence around the filter resonances thenallows for tuning the coupling type and strength. Originally limited to smallrotation angles, we show how the validity range of the filter description canbe extended to the long time limit by time-sliced evolution sequences. Based onthat insight, the construction of tunable, noise decoupled, conditional gatescomposed of alternating pulse sequences is proposed. In particular such anapproach can lead to a significant improvement in fidelity as compared to astrictly periodic control sequence. Moreover we analyze the decoherence impact,the relation to the filter for classical noise known from dynamical decouplingsequences, and we outline how an alternating sequence can improve spin sensingprotocols.

Filter design for hybrid spin gates