  Electron and nuclear spins of diamond nitrogen-vacancy (NV) centers are good
candidates for quantum information processing as they have long coherence time
and can be initialized and read out optically. However, creating a large number
of coherently coupled and individually addressable NV centers for quantum
computing has been a big challenge. Here we propose methods to use high-density
diamond NV centers coupled by spin-spin interaction with an average separation
on the order of 10 nm for quantum computing. We propose to use a strain
gradient to encode the position information of each NV center in the energy
level of its excited electron orbital state, which causes a shift of its
optical transition frequency. With such strain encoding, more than 100
closely-packed NV centers below optical diffraction limit can be read out
individually by resonant optical excitation. A magnetic gradient will be used
to shift the electron spin resonant (ESR) frequencies of NV centers. Therefore,
the spin state of each NV center can be individually manipulated and different
NV centers can be selectively coupled. A universal set of quantum operations
for two-qubit and three-qubit system is introduced by careful design of
external drives. Moreover, entangled states with multiple qubits can be created
by this protocol, which is a major step towards quantum information processing
with solid-state spins.
