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[[Image:L-alanine-3D-balls.png|thumb|260px|[[Molecule]] of [[alanine]] used in [[Nuclear magnetic resonance|NMR]] implementation of quantum computing. [[Qubit]]s are implemented by [[spin (physics)|spin]] [[Quantum state|states]] of the black [[carbon]] [[atom]]s]]
'''NMR quantum computing''' uses the [[spin (physics)|spin]] states of molecules as [[qubit]]s. NMR differs from other implementations of quantum computers in that it uses an [[quantum ensemble|ensemble]] of systems, in this case molecules. The ensemble is initialized to be the thermal equilibrium state (see [[quantum statistical mechanics]]). In mathematical parlance, this state is given by the [[density matrix]]:
:<math> \rho = \frac{e^{- \beta H}}{\operatorname{Tr}(e^{- \beta H})}, </math>
where ''H'' is the hamiltonian matrix of an individual molecule and

:<math> \beta = \frac{1}{k \, T}</math>

where <math>k</math> is the [[Boltzmann constant]] and <math>T</math> the temperature.

Operations are performed on the ensemble through RF pulses applied perpendicular to a strong, static field, created by a very large magnet. See [[Nuclear Magnetic Resonance]].

Some early success was obtained in performing quantum algorithms in NMR systems due to the relative maturity of NMR technology. For instance, in 2001 researchers at IBM reported the successful implementation of [[Shor's algorithm]] in a 7-[[qubit]] NMR quantum computer.<ref>{{cite journal |author=Vandersypen LMK, Steffen M, Breyta G, Yannoni CS, Sherwood MH, Chuang IL |year=2001 |title=Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance |journal=Nature |volume=414 |issue=6866 |pages=883–887 |doi=10.1038/414883a |pmid=11780055|arxiv = quant-ph/0112176 |bibcode = 2001Natur.414..883V }}</ref>

However, even from the early days, it was recognized that NMR quantum computers would never be very useful due to the poor scaling of signal to noise in such systems.<ref>{{cite journal |author=Warren WS |year=1997 |title=The usefulness of NMR quantum computing |journal=Science |volume=277 |issue=5332 |pages=1688–1689 |url=http://www.sciencemag.org/content/277/5332/1688.full |doi=10.1126/science.277.5332.1688}}</ref> More recent work, particularly by Caves and others, shows that all experiments in liquid state bulk ensemble NMR quantum computing to date do not possess quantum entanglement, thought to be required for quantum computation. Hence NMR quantum computing experiments are likely to have been only classical simulations of a quantum computer.<ref>{{cite journal |author=Menicucci NC, Caves CM |year=2002 |title=Local realistic model for the dynamics of bulk-ensemble NMR information processing |journal=Physical Review Letters |volume=88 |issue=16 |doi=10.1103/PhysRevLett.88.167901|arxiv = quant-ph/0111152 |bibcode = 2002PhRvL..88p7901M }}</ref>

==References==
{{Reflist}}

{{quantum computing}}
[[Category:Quantum information science]]

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en>Trovatore: restore the good spelling correction