It has been shown that quantum computers can exceed the computational efficiency of classical computer especially for certain tasks, such as prime factorization , quantum simulations, and database searches.  As it has been verified experimentally that quantum computers can be built through bulk spin-resonance method via NMR on bulk liquids  up to several qubits, there has been increasing interests on physical realization of quantum computers. However, spin-resonance method based on NMR is hard to be extended above 10 qubits, since the measurable signal is considerably decreased as the number of qubit increases.  In order to overcome the difficulties in scaling-up problem, a conceptual design for solid-state quantum computers based on 31P doped in bulk Si has been proposed.  From the arrays of 31P, which has _ nuclear spin and will be a single qubit, quantum computer can be realized. This model, however, has crucial experimental obstacles to realize such that it needs arrays of 31P within atomic level accuracy. Therefore, we have proposed a design that fullerenes encapsulate _ nuclear spin atomic dopants for the fabricating arrays of _ nuclear spin particle in solid-state materials.  We have reported two possible models, which are 1H @ C20H20 and 31P in diamond nanocrystallite generated by compressed bucky onion, from the studies of 1H or 31P @ various fullerenes. 
In this work, we have further examined those two candidates for quantum computers. First, we have studied the fabrication pathways of both candidates such that we have examined diamond cluster formed from bucky onion due to compression, and endo-fullerene with hydrogen atom in C20H20. Second, we have investigated stability of the systems, for example, positions and diffusions of 1H and 31P. And it has been revealed that dopants are stable at desired sites for each model such that 1H prefers to stay at the center of C20H20 and 31P at the substitutional site in diamond. Third, we have examined the electronic structure of the dopants atoms, which is one of the most important factors for the models to work as quantum computers. We will also discuss the possible ways to fabricate the arrays of either 1H @ C20H20 or 31P-doped diamond Nanocrystallite. All the work presented here is studied either by total energy pseudo-potential density functional theory method or by molecular dynamics using Tersoff-Brenner potential method.
Ekert, A. and Jozsa, R., Rev. Mod. Phys.68, 733 (1996)