Generalized dynamical decoupling sequences for improved electron-nuclear entangling gates in defect systems

We design electron-nuclear gates applicable to defects in diamond or silicon carbide for arbitrary electron spin systems. We go beyond the standard CPMG and UDD dynamical decoupling sequences by allowing arbitrary interpulse spacings and rotations on the electronic spin. We study the range of entangling gates we can generate and the effect of unwanted spins on the target evolution. We quantify the selectivity of our sequences via multipartite entanglement measures, which capture the complete dynamical evolution of the system.