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

Quantum information processing with closely-spaced diamond color centers in strain and magnetic fields