  Steps towards implementing a collision based two-qubit gate in optical
lattices have previously been realized by the parallel merging all pairs of
atoms in a periodicity two superlattice. In contrast, we propose an
architecture which allows for the merger of a selected qubit pair in a novel
long-periodicity superlattice structure consisting of two optical lattices with
close-lying periodicity. We numerically optimize the gate time and fidelity,
including the effects on neighboring atoms, and in the presence of experimental
sources of error. Furthermore, the superlattice architecture induces a
differential hyperfine shift, allowing for single-qubit gates. The fastest
possible single-qubit gate times, given a maximal tolerable rotation error on
the remaining atoms at various values of the lattice wavelengths, are
identified. We find that robust single- and two-qubit gates with gate times of
a few 100~$\mu$s and with error probabilities $\sim{}10^{-3}$ are possible.
