Robust control of entanglement in a nitrogen-vacancy center coupled to a ¹³C nuclear spin in diamond

We address the problem of generating a robust entangling gate between electronic and nuclear spins in a system of a single nitrogen-vacancy center coupled to a nearest ¹³C atom in diamond against certain types of systematic errors such as pulse-length and off-resonance errors. We analyze the robustness of various control schemes: sequential pulses, composite pulses and numerically optimized pulses. We find that numerically optimized pulses, produced by the modified gradient ascent pulse engineering (GRAPE) algorithm, are more robust than the composite pulses and the sequential pulses. The optimized pulses can also be implemented in a faster time than the composite pulses.