NMR quantum computing, history and limits

Short answer: Liquid-state nuclear magnetic resonance was the first technology to run small quantum computations, and its own researchers have long said it does not scale. A 1998 Royal Society paper shows quantum computation with mixed states, a 2000 arXiv paper argues liquid-state NMR is unlikely to give practical quantum computers, and a more recent review calls NMR the best technology for simple experiments and the worst for large-scale machines. This post is a history, not a current hardware claim.

1998: computation with mixed states

The Royal Society paper (Proceedings A, 1998) shows that quantum computation is possible with mixed states instead of pure states as inputs. The method embeds in the mixed state a subspace that transforms like a pure state and can be identified by labelling it through logical (spin), temporal or spatial degrees of freedom. The authors say this permits quantum computation with bulk ensembles far from the ground state. They present experimental results for quantum gates and circuits implemented with liquid-state nuclear magnetic resonance and verified by quantum state tomography.

2000: the scaling problem

A February 2000 arXiv paper says liquid-state NMR techniques had produced some spectacular successes in constructing small quantum computers and that NMR was by far the leading technology for quantum computation at the time. The authors say there are significant problems with any attempt to scale it up to computers of useful size. They say some may be sidestepped in the next few years, but it is unlikely that all will be solved, so current liquid-state NMR techniques are unlikely to be a viable technology for practical quantum computation.

A later review

A review in a ScienceDirect journal says NMR is arguably both the best available quantum technology for simple quantum computing experiments and the worst technology ever seriously put forward for large-scale quantum computers. It says that after a few years of rapid growth, which led to an implementation of Shor's factoring algorithm in a seven-spin system, the field reached its natural limits and progress became challenging. Interest has since largely moved to precise and efficient manipulation of spin states, with the aim of developing methods for more scalable technologies and for conventional NMR. The review adds that NMR implementations remain popular for proof-of-principle demonstrations of simple quantum information protocols because they are user friendly.

Limits

The three pages are abstracts, so details of how the scaling problems arise are not covered here. The 2000 paper's expectation about the next few years was a prediction, and the review is the later assessment.

FAQ

Did NMR quantum computers work?

For small demonstrations, yes. The 1998 paper reports gates and circuits verified by state tomography, and the review mentions Shor's algorithm in a seven-spin system.

Why did NMR fall out of favour for computing?

The authors of the 2000 paper and the review both point to problems scaling to useful sizes.

What is a pseudo-pure or mixed-state approach?

The 1998 paper embeds a subspace inside a mixed state that behaves like a pure state, so ensembles far from the ground state can compute.

Is NMR still used?

The review says it remains popular for proof-of-principle demonstrations of simple protocols.

Is NMR used to build large quantum computers today?

The review says it is among the worst technologies for that.