Ensemble Quantum Computing by NMR Spectroscopy

A quantum computer (QC) can operate in parallel on all its possible inputs at once, but the amount of information that can be extracted from the result is limited by the phenomenon of wave function collapse. We present a new computational model, which differs from a QC only in that the result of a m...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 1997-03, Vol.94 (5), p.1634-1639
Main Authors: Cory, David G., Fahmy, Amr F., Havel, Timothy F.
Format: Article
Language:English
Subjects:
Chemical Phenomena
Chemistry
Computer programming
Computer science
Computing Methodologies
Energy levels
Expected values
Hilbert spaces
Liquids
Magnetic Resonance Spectroscopy - methods
Mathematical vectors
Molecules
NMR
Nuclear magnetic resonance
Physical Phenomena
Physical Sciences
Physics
Polynomials
Quantum computers
Quantum Theory
Spectroscopy
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Summary:A quantum computer (QC) can operate in parallel on all its possible inputs at once, but the amount of information that can be extracted from the result is limited by the phenomenon of wave function collapse. We present a new computational model, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof. Such an expectation value QC can solve nondeterministic polynomial-time complete problems in polynomial time. This observation is significant precisely because the computational model can be realized, to a certain extent, by NMR spectroscopy on macroscopic ensembles of quantum spins, namely molecules in a test tube. This is made possible by identifying a manifold of statistical spin states, called pseudo-pure states, the mathematical description of which is isomorphic to that of an isolated spin system. The result is a novel NMR computer that can be programmed much like a QC, but in other respects more closely resembles a DNA computer. Most notably, when applied to intractable combinatorial problems, an NMR computer can use an amount of sample, rather than time, which grows exponentially with the size of the problem. Although NMR computers will be limited by current technology to exhaustive searches over only 15 to 20 bits, searches over as much as 50 bits are in principle possible, and more advanced algorithms could greatly extend the range of applicability of such machines.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.94.5.1634