Coupling-selective quantum optimal control in weak-coupling NV-\(^{13}\)C system

Quantum systems are under various unwanted interactions due to their coupling with the environment. Efficient control of quantum system is essential for quantum information processing. Weak-coupling interactions are ubiquitous, and it is very difficult to suppress them using optimal control method, because the control operation is at a time scale of the coherent life time of the system. Nitrogen-vacancy (NV) center of diamond is a promising platform for quantum information processing. The \(^{13}\)C nuclear spins in the bath are weakly coupled to the NV, rendering the manipulation extremely difficulty. Here, we report a coupling selective optimal control method that selectively suppresses unwanted weak coupling interactions and at the same time greatly prolongs the life time of the wanted quantum system. We applied our theory to a 3 qubit system consisting of one NV electron spin and two \(^{13}\)C nuclear spins through weak-coupling with the NV center. In the experiments, the iSWAP\(^{\dagger }\) gate with selective optimal quantum control is implemented in a time-span of \(T_{ctrl}\)= 170.25 \(\mu\)s, which is comparable to the phase decoherence time \(T_2\)= 203 \(\mu s\). The two-qubit controlled rotation gate is also completed in a strikingly 1020(80) \(\mu\)s, which is five times of the phase decoherence time. These results could find important applications in the NISQ era.