  We demonstrate storage and manipulation of one qubit encoded into a
decoherence-free subspace (DFS) of two nuclear spins using liquid state nuclear
magnetic resonance (NMR) techniques. The DFS is spanned by states that are
unaffected by arbitrary collective phase noise. Encoding and decoding
procedures reversibly map an arbitrary qubit state from a single data spin to
the DFS and back. The implementation demonstrates the robustness of the DFS
memory against engineered dephasing with arbitrary strength as well as a
substantial increase in the amount of quantum information retained, relative to
an un-encoded qubit, under both engineered and natural noise processes. In
addition, a universal set of logical manipulations over the encoded qubit is
also realized. Although intrinsic limitations prevent maintaining full noise
tolerance during quantum gates, we show how the use of dynamical control
methods at the encoded level can ensure that computation is protected with
finite distance. We demonstrate noise-tolerant control over a DFS qubit in the
presence of engineered phase noise significantly stronger than observed from
natural noise sources.
