Nuclear magnetic resonance (NMR) quantum computing

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Molecule of alanine used in NMR implementation of quantum computing. Qubits are implemented by spin states of carbon atoms (numbered)

NMR quantum computing 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. 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:

$\rho = \frac{e^{- \beta H}}{\operatorname{Tr}(e^{- \beta H})},$

where H is the hamiltonian matrix of an individual molecule and

$\beta = (\mbox{Boltzmann constant} \cdot \mbox{temperature})^{-1} = \frac{1}{k \, T}$

Operations are performed on the ensemble through magnetic 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[1].

[edit] References

Lieven M. K. Vandersypen, Matthias Steffen, Gregory Breyta, Costantino S. Yannoni, Mark H. Sherwood and Isaac L. Chuang (2001). "Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance". Nature 414: 883–887.

Quantum computing
Qubit \| Quantum circuit \| Quantum computer \| Quantum cryptography \| Quantum information \| Quantum programming \| Quantum teleportation \| Quantum virtual machine \| Timeline of quantum computing
Quantum algorithms
Deutsch-Jozsa algorithm \| Grover's search \| Shor's factorization
Nuclear magnetic resonance (NMR) quantum computing
Liquid-state NMR QC \| Solid-state NMR QC
Photonic computing
Nonlinear optics \| Linear optics QC \| Non-linear optics QC \| Coherent state based QC
Trapped ion quantum computer
NIST-type ion-trap QC \| Austria-type ion-trap QC
Semiconductor-based quantum computing
Kane QC \| Loss-DiVincenzo QC
Superconducting quantum computing
Charge qubit \| Flux qubit \| Hybrid qubits