  Universal ion trap computation on Decoherence Free Subspaces (DFS) using only
two qubit operations is presented. The DFS is constructed for the collective
dephasing model. Encoded single and two-qubit logical operations are
implemented via the Sorensen-Molmer interaction. Alternation of the effective
Hamiltonians for two particular phase configurations of control fields
approximates an anisotropic exchange interaction. This is universal over
suitable encodings of one logical qubit into three physical qubits which are
also DFS under collective decoherence.
