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Concept
Nuclear magnetic resonance quantum computer
Summary
Nuclear magnetic resonance quantum computing (NMRQC) is one of the several proposed approaches for constructing a quantum computer, that uses the spin states of nuclei within molecules as qubits. The quantum states are probed through the nuclear magnetic resonances, allowing the system to be implemented as a variation of nuclear magnetic resonance spectroscopy. 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.
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 This approach has since been superseded by solid state NMR (SSNMR) as a means of quantum computation.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 in which some of its atom's nuclei behave as spin-1⁄2 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).
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Quantum computing
A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.