  Liquid phase NMR is a general purpose test-bed for developing methods of
coherent control relevant to quantum information processing. Here we extend
these studies to the coherent control of logical qubits and in particular to
the unitary gates necessary to create entanglement between logical qubits. We
report an experimental implementation of a conditional logical gate between two
logical qubits that are each in decoherence free subspaces that protect the
quantum information from fully correlated dephasing.
