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. doi:10.1038/414883a.

v • d • e Quantum computing

General	Qubit • Quantum computer • Quantum information • Quantum programming • Quantum virtual machine • Timeline of quantum computing

Quantum communication	Quantum channel • Quantum cryptography • Quantum teleportation • LOCC • Entanglement distillation

Quantum algorithms	Universal quantum simulator • Deutsch-Jozsa algorithm • Grover's search • Shor's factorization • Simon's Algorithm • (BQP)

Quantum computing models	Quantum circuit (quantum gate) • One-way quantum computer (cluster state) • Adiabatic quantum computation

Decoherence prevention	Quantum error correction • Topological quantum computer

Physical implementations

Quantum optics	Linear optics QC • Cavity QED

Ultracold atoms	Trapped ion quantum computer • Optical lattice

Spin-based	Nuclear magnetic resonance (NMR) quantum computing • Kane QC • Loss-DiVincenzo (quantum dot) QC

Other	Superconducting quantum computing (Charge qubit • Flux qubit) • Nitrogen-vacancy center