Quantum Computing with Endohedral Fullerenes

We review the present state of the art in using the endohedral fullerenes N@C60 and P@C60 as qubits in a spin quantum computer. After a brief introduction to spin quantum computing, we first discuss the rich spin structure of these endohedral fullerenes and specific theoretical proposals for architectures and operation models leading to a scalable quantum computer. We then briefly discuss those aspects of materials science that are needed to realize the proposed architectures. The central part of this chapter is a review of quantum operations and entanglement realized with endohedral fullerenes. Finally, we review efforts to realize single spin detection of endohedral fullerenes and conclude with a brief outlook on outstanding problems to be solved for obtaining a scalable quantum register.