Nuclear-nuclear interaction mediated by a mechanically controlled nitrogen-vacancy-center spin in diamond

We propose a scheme to achieve nuclear-nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy (NV) center in diamond. Here we demonstrate two-qubit entangling gates and quantum-state transfer between two carbon nuclei in diamond. In such a system, the NV center interacts with a nearby nuclear spin via a dipole-dipole interaction. Under the quantum Zeno condition, the scheme is robust against decoherence caused by coupling between the NV center (nuclear spins) and the environment. Conveniently, precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center. Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication in a polygon geometry with each vertex occupied by a nuclear spin.Comment: 11 pages, 8 figure