The ideal picture of liquid state NMR (LSNMR) quantum information processing (QIP) is based on a molecule in which some of its atom's nuclei behave as spin-½ systems. Depending on which nuclei we are considering they will have different energy levels and different interaction with its neighbours and so we can treat them as distinguishable qubits. In this system we tend to consider the inter-atomic bonds as the source of interactions between qubits and exploit these spin-spin interactions to perform 2-qubit gates such as CNOTs that are necessary for universal quantum computation. In addition to the spin-spin interactions native to the molecule an external magnetic field can be applied (in NMR laboratories) and these impose single qubit gates. By exploiting the fact that different spins will experience different local fields we have control over the individual spins.
The picture described above is far from realistic since we are treating a single molecule. NMR is performed on an ensemble of molecules, usually with as many as 10^15 molecules. This introduces complications to the model, one of which is introduction of decoherence. In particular we have the problem of an open quantum system interacting with a macroscopic number of particles near thermal equilibrium (~mK to ~300 K). This has led the development of decoherence suppression techniques that have spread to other disciplines such as trapped ions. The other significant issue with regards to working close to thermal equilibrium is the mixedness of the state. This required the introduction of ensemble quantum processing, whose principal limitation is that as we introduce more logical qubits into our system we require larger samples in order to attain discernable signals during measurement.