  This letter presents a two-dimensional nuclear magnetic resonance(NMR)
approach for constructing a two-logical-qubit decoherence-free subspace (DFS)
based on the fact that the three protons in a CH3 spin system can not be
resolved in one-dimension NMR spectroscopy, but to a certain extent, can be
distinguished by two-dimensional multiple-quantum NMR. We used four noisy
physical nuclear spins, including three protons and one carbon in the CH3 spin
system, to generate two decoherence-free logical quantum bits. It made full use
of the unaddressed spins which could not be used in one-dimensional spectrum.
Furthermore, we have experimentally demonstrated such an approach. Our
experimental results have shown that our DFS can protect against far more types
of decoherence than the one composed of four noisy physical qubits all with
different chemical shifts. More importantly, this idea may provide new insights
into extending qubit systems in the sense that it effectively utilizes the
magnetically equivalent nuclei.
