Large-scale cluster state generation with nuclear spins in diamonds

The cluster state is an indispensable resource for one-way quantum computing (1WQC). We propose a practical scheme for constructing cluster states among nuclear spins in nitrogen-vacancy defect centres (NV centres) in different diamonds. The entanglement of nuclear spins within an NV centre is made by hyperfine coupling via electron spin, and the entanglement between remote NV centres is accomplished using the parity projection of emitted photons. We discus the possibility to build large-scale nuclear-spin cluster states with diamonds.