Optically addressable universal holonomic quantum gates on diamond spins

Microwave-driven holonomic quantum gates on an optically selected electron spin in a nitrogen-vacancy centre in diamond are demonstrated. Optically addressable entanglement is generated between the electron and adjacent nitrogen nuclear spin. The ability to individually control the numerous spins in a solid-state crystal is a promising technology for the development of large-scale quantum processors and memories. A localized laser field offers spatial selectivity for electron spin manipulation through spin-obit coupling, but it has been difficult to simultaneously achieve precise and universal manipulation. Here, we demonstrate microwave-driven holonomic quantum gates on an optically selected electron spin in a nitrogen-vacancy centre in diamond. The electron spin is precisely manipulated with global microwaves tuned to the frequency shift induced by the local optical Stark effect. We show the universality of the operations, including state initialization, preparation, readout and echo. We also generate optically addressable entanglement between the electron and adjacent nitrogen nuclear spin. High-fidelity operations are achieved by applying amplitude-alternating pulses, which are tolerant to fluctuations in microwave intensity and detuning. These techniques enable site-selective quantum teleportation transfer from a photon to a nuclear spin memory, paving the way for the realization of distributed quantum computers and the quantum Internet with large-scale quantum storage.