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

Abstract Quantum systems are under various unwanted interactions due to their coupling with the environment. Efficient control of quantum system is essential for information processing. Weak-coupling ubiquitous, and it very difficult suppress them using optimal method, because operation at a time scale coherent life system. Nitrogen-vacancy (NV) center diamond promising platform The $$^{13}$$ 13 C nuclear spins in bath weakly coupled NV, rendering manipulation extremely difficulty. Here, we report selective method that selectively suppresses weak same greatly prolongs wanted We applied our theory 3 qubit consisting one NV electron spin two through weak-coupling center. In experiments, iSWAP $$^{\dagger }$$ † gate implemented time-span $$T_{ctrl}$$ T ctrl = 170.25 $$\mu$$ μ s, which comparable phase decoherence $$T_2$$ 2 203 $$\mu s$$ s . two-qubit controlled rotation also completed strikingly 1020(80) five times time. These results could find important applications NISQ era.