We propose a scheme to implement the two-qubit gates between the nuclear spins of the encapsulated atoms in endohedral fullerenes ${}^{15}\mathrm{N}@{\mathrm{C}}_{60}$ or ${}^{31}\mathrm{P}@{\mathrm{C}}_{60}$, within today’s magnetic resonance techniques. Since there is no interaction between the nuclear spins, this scheme employs the electronic spins as medium and two swap operations are proposed to transfer the information between the nuclear spin $\frac{1}{2}$ and the electronic spin $\frac{3}{2}$, and between two electronic spins $\frac{3}{2}$. These two-qubit gates, along with the single-qubit rotation gates, compose a universal set of quantum gates in fullerene-based quantum computation.

• Received 18 August 2006

DOI:https://doi.org/10.1103/PhysRevA.75.012318