Nuclear magnetic resonance quantum computer

Nuclear Magnetic Resonance (NMR) quantum computing is one of the several proposed approaches for constructing a quantum computer, that uses the spin states of molecules as qubits. NMR differs from other implementations of quantum computers in that it uses an ensemble of systems, in this case molecules, rather than a single pure state qubit.

Initially the approach was to use the spin properties of atoms of particular molecules in a liquid sample as qubits - this is known as liquid state NMR (LSNMR). This approach has since been superseded by solid state NMR (SSNMR) as a means of quantum computation.

The ideal picture of liquid state NMR (LSNMR) quantum information processing (QIP) is based on a molecule of 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.

Solid state NMR (SSNMR) differs from LSNMR in that we have a solid state sample, for example a nitrogen vacancy diamond lattice rather than a liquid sample. This has many advantages such as lack of molecular diffusion decoherence, lower temperatures can be achieved to the point of suppressing phonon decoherence and a greater variety of control operations that allow us to overcome one of the major problems of LSNMR that is initialisation. Moreover, as in a crystal structure we can localize precisely the qubits, we can measure each qubit individually, instead of having an ensamble measurement as in LSNMR.

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