  We propose a new quantum-computing scheme using ultracold neutral ytterbium
atoms in an optical lattice. The nuclear Zeeman sublevels define a qubit. This
choice avoids the natural phase evolution due to the magnetic dipole
interaction between qubits. The Zeeman sublevels with large magnetic moments in
the long-lived metastable state are also exploited to address individual atoms
and to construct a controlled-multiqubit gate. Estimated parameters required
for this scheme show that this proposal is scalable and experimentally
feasible.
