Nuclear magnetic resonance quantum computer

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.

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.

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.

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).

[4][5][6] Manipulation of nuclear spins for quantum computing using liquid state NMR was introduced independently by Cory, Fahmy and Havel[7][8] and Gershenfeld and Chuang[9] in 1997.

For instance, in 2001 researchers at IBM reported the successful implementation of Shor's algorithm in a 7-qubit NMR quantum computer.

[10] However, even from the early days, it was recognized that NMR quantum computers would never be very useful due to the poor scaling of the signal-to-noise ratio in such systems.

Considering the molecules in the liquid sample to contain two spin-⁠1/2⁠ nuclei, the system Hamiltonian will have two chemical shift terms and a dipole coupling term: Control of a spin system can be realized by means of selective RF pulses applied perpendicular to the quantization axis.

For detailed examples of the effects of pulses on such a spin system, the reader is referred to Section 2 of work by Cory et al.[13]