Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate

Rabi nutations of a single nuclear spin in a solid have been observed. The experiments were carried out on a single electron and a single ${}^{13}\mathrm{C}$ nuclear spin of a single nitrogen-vacancy defect center in diamond. The system was used for implementation of quantum logical NOT and a conditional two-qubit gate (CROT). Density matrix tomography of the CROT gate shows that the gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms.