  We introduce protocols for designing and manipulating qubits with ultracold
alkali atoms in 3D optical lattices. These qubits are formed from two-atom spin
superposition states that create a decoherence-free subspace immune to stray
magnetic fields, dramatically improving coherence times while still enjoying
the single-site addressability and Feshbach resonance control of
state-of-the-art alkali atom systems. Our protocol requires no continuous
driving or spin-dependent potentials, and instead relies upon the population of
a higher motional band to realize naturally tunable in-site exchange and
cross-site superexchange interactions. As a proof-of-principle example of their
utility for entanglement generation for quantum computation, we show the
cross-site superexchange interactions can be used to engineer 1D cluster
states. Explicit protocols for experimental preparation and manipulation of the
qubits are also discussed, as well as methods for measuring more complex
quantities such as out-of-time-ordered correlation functions (OTOCs).
