  In quantum information processing, one of the most useful interaction between
qubits is the Ising type interaction. We propose a scheme to implement the
exact Ising interaction through magnetic dipole-dipole interaction. Although
magnetic dipolar interaction is Heisenberg type in general, this interaction
can bring about the exact mathematical form of the Ising interaction if qubit
levels are chosen among the highest magnetic quantum number states. Real
physical systems to which our scheme can be applied include rotational states
of molecules, hyperfine states of atoms, or electronic states of
nitrogen-vacancy centers in diamond. We analyze the feasibility of our scheme
for these systems. For example, when the hyperfine levels of rubidium 87 atoms
are chosen as qubits and the distance of the two atoms is 0.1 micrometer,
controlled-Z gate time will be 8.5 ms. We suggest diverse search and study to
achieve optimal implementation of this scheme.
