Numerical Optimization of Microwave and Radio Frequency Control Pulses for the Nitrogen-Vacancy Electron-Nuclear Spin Register

Numerical optimizations of the microwave and radio frequency control pulses for the nitrogen vacancy electron-nuclear spin register were performed by means of a gradient ascent pulse engineering method (GRAPE). Three examples of spin control — specific quantum state preparation and the implementation of a controlled-NOT and unconditional - gate have been optimized through parallel computation. The optimized control pulses reach fidelities of F = 0:99944, F = 0:77929 and F = 0:99143 respectively, whereas simulation of Rabi oscillation based control yields corresponding results of F = 0:96325, F = 0:21884 and F = 0:42702. The fixed step size in the GRAPE algorithm imposes a tradeoff between monotone and fast convergence of optimized control pulses and the unspecific performance function may lead to erroneous optimizations. These complications require future research to be resolved. Furthermore, implementing the effect of decoherence yields no significant average fidelity improvement, but has a positive effect on reducing the spread of final density states for the case of quantum state preparation.