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Cited by 964Quantum Computing Algorithms and ArchitectureDNA and Biological ComputingAdvanced NMR Techniques and Applications

Ensemble quantum computing by NMR spectroscopy

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Cory, David G., Fahmy, Amr F., Havel, Timothy F.·1997·Proceedings of the National Academy of Sciences
DOI 10.1073/pnas.94.5.1634PMC PMC19968
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Abstract

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.

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  • Using the methods of Cory et al., it is possible to create an effective pure state that behaves equivalently to |00>.

    “Using the methods of Cory et al. 5 it is, however, possible to create an effective pure state, which behaves in an equivalent manner.”

    From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [5]

  • Only two methods have been used to demonstrate quantum logic gates: ion traps and nuclear magnetic resonance (NMR).

    “only two methods have been used to demonstrate quantum logic gates: ion traps, 3, 4 and nuclear magnetic resonance (NMR). 5, 6”

    From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [5]

  • Nuclear spins are particularly good quantum bits because of their natural isolation from the environment, and their use for quantum computation is possible by applying NMR techniques in an unconventional manner.

    “because of their natural isolation from the environment, nuclear spins are particularly good 'quantum bits' 16 , and their use for quantum computation is possible by applying nuclear magnetic resonance (NMR) techniques in an unconventional manner 17-19 .”

    From Experimental realization of a quantum algorithm (1998) · cites this paper as [19]

  • The effective pure state ρ1 is a suitable initial state for Shor's algorithm because it generates the same signal as |ψ1〉 up to a proportionality constant.

    “We converted ρ th into a 7-spin effective pure state [11, 12] ρ 1 via temporal averaging [9] (step 0); ρ 1 constitutes a suitable initial state for Shor's factoring algorithm since it generates the same signal as | ψ 1 〉 , up to a proportionality constant [11, 12].”

    From Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance (2001) · cites this paper as [12]

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Research works printed but not linked: 19

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Cited by

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Authors
Cory, D. G., Fahmy, A. F., & Havel, T. F.
Affiliations
Harvard University (US)
ORCID
Venue
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences
Published
1997-03-04
Volume
94
Issue
5
Pages
1634-1639
ISSN
  • 0027-8424 (ISSN-L)
  • 1091-6490
DOI
10.1073/pnas.94.5.1634
PMC
PMC19968
OpenAlex
W2067120233
Cited by
964
References
3
Citations by year
2026: 9 · 2025: 19 · 2024: 21 · 2023: 31 · 2022: 32 · 2021: 28 · 2020: 27 · 2019: 23 · 2018: 16 · 2017: 28 · 2016: 37 · 2015: 24 · 2014: 20 · 2013: 26 · 2012: 23
FWCI
61.98
Type
journal article
Language
en
Open access
Locations
  • Proceedings of the National Academy of Sciences (publishedVersion)
  • Europe PMC (PubMed Central) (publishedVersion)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › DNA and Biological Computing
  • Physical Sciences › Chemistry › Spectroscopy › Advanced NMR Techniques and Applications
Keywords
NMR spectroscopy, pseudo-pure states, wave function collapse, NP-complete problems, combinatorial optimization, DNA computing
MeSH terms
Chemistry, Computing Methodologies, Magnetic Resonance Spectroscopy, Physics, Quantum Theory, Physical Phenomena, Chemical Phenomena

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