same time, this method is somewhat sensitive to collisional losses when two atoms in the $^3$P$_0$ manifold collide, as the near-resonant lattices will always produce admixtures of this state. However, this is only an issue during the short times involved in gate operations, and is strongly suppressed in a realistic setup where atoms are also AC-Stark shifted, as discussed below. Nuclear-spin-dependent lattices would also have immediate applications in quantum simulation [@Cazalilla; @Gorshkov; @Hermele2009; @FossFeig; @Gerbier2010]. In particular, the degeneracy in models with SU(N) symmetry [@Cazalilla; @Gorshkov; @Hermele2009] (which can be studied using alkaline-earth-like atoms by making use of the symmetry for interactions of atoms in different nuclear spin levels) could be deliberately broken and restored by applying these nuclear-spin-dependent potentials.

The rest of this article is organised as follows: We first discuss the formation of near-resonant spin-dependent optical lattices in more detail in Sec II, together with preparation of atomic registers in these lattices. In Sec. III we then discuss means for readout of individual qubits, and in Sec IV we treat ideas for gate schemes to entangle two qubits, including making use of lossy blockade mechanisms. In Sec. V we present a summary and outlook.

Spin-dependent Adiabatic potentials {#sec:potentials}
