In the field of quantum physics, quantum control is essential. Precise and efficient quantum control is a prerequisite for the experimental research using quantum systems, and it is also the basis for applications such as in quantum computing and quantum sensing. As a solid-state spin system, the nitrogen-vacancy (NV) center in diamond has a long coherence time at room temperature. It can be initialized and read out by optical methods, and can achieve universal quantum control through the microwave field and radio frequency fields. It is an excellent experimental platform for studying quantum physics. In this review, we introduce the recent results of quantum control in NV center and discuss the following parts: 1) the physical properties of the NV center and the realization method of quantum control, 2) the decoherence mechanism of the NV center spin qubit, and 3) the application of single-spin quantum control and relevant research progress.
Zero-field nuclear magnetic resonance (NMR) provides complementary analysis modalities to those of high-field NMR and allows for ultra-high-resolution spectroscopy and measurement of untruncated spin-spin interactions. Unlike for the high-field case, however, universal quantum control -- the ability to perform arbitrary unitary operations -- has not been experimentally demonstrated in zero-field NMR. This is because the Larmor frequency for all spins is identically zero at zero field, making it challenging to individually address different spin species. We realize a composite-pulse technique for arbitrary independent rotations of
1H and
13C spins in a two-spin system. Quantum-information-inspired randomized benchmarking and state tomography are used to evaluate the quality of the control. We experimentally demonstrate single-spin control for
13C with an average gate fidelity of
0.9960(2) and two-spin control via a controlled-not (CNOT) gate with an estimated fidelity of
0.99. The combination of arbitrary single-spin gates and a CNOT gate is sufficient for universal quantum control of the nuclear spin system. The realization of complete spin control in zero-field NMR is an essential step towards applications to quantum simulation, entangled-state-assisted quantum metrology, and zero-field NMR spectroscopy.