(color online) Noise-resilient quantum gates implemented by DD. (a) Propagator evolution in the conventional settings of FID or periodic CPMG sequence in the operator space. (b) In contrast to the conventional schemes, one can relax the timing constraint in applying the DD pulses and thereby steer the system propagator to the desired points in the operator space. For instance, the C-NOT and the nuclear qubit Pauli-X (Xn) gates can be realized by the purple and the yellow paths, respectively. The gate is characterised by performing state tomography of the two-qubit system before and after its implementation. (c) State tomography for the initial state . (d) Schematic diagram of the conditional evolution of the (upper panel) and (lower panel) states steered by the DD. (e) State tomography of the output Bell state for the initial state in (c). Reproduced from Ref. [32], NPG.