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Electron Spin Resonance (ESR) Based Quantum Computing pp 193–226Cite as

NMR Quantum Information Processing

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Part of the book series: Biological Magnetic Resonance ((BIMR,volume 31))

Abstract

Quantum computing exploits fundamentally new models of computation based on quantum mechanical properties instead of classical physics, and it is believed that quantum computers are able to dramatically improve computational power for particular tasks. At present, nuclear magnetic resonance (NMR) has been one of the most successful platforms amongst all current implementations. It has demonstrated universal controls on the largest number of qubits, and many advanced techniques developed in NMR have been adopted to other quantum systems successfully. In this review, we show how NMR quantum processors can satisfy the general requirements of a quantum computer, and describe advanced techniques developed towards this target. Additionally, we review some recent NMR quantum processor experiments. These experiments include benchmarking protocols, quantum error correction, demonstrations of algorithms exploiting quantum properties, exploring the foundations of quantum mechanics, and quantum simulations. Finally we summarize the concepts and comment on future prospects.

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Notes

  1. 1.

    For simplicity, we only consider spin ½ systems in this chapter.

  2. 2.

    The Clifford group is the group of unitary operations that leave take Pauli operators to Pauli operators.

  3. 3.

    In general, a protected space does not necessarily encode a single qubit, and single qubit gates are often not transversal.

  4. 4.

    The argument regarding the number of elements to be summed is somewhat simplistic, since we only require an estimate. Nevertheless, there is good reason to expect the computation scale exponentially with n [78].

  5. 5.

    Strictly speaking, it should also be scalable.

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Acknowledgement

We thank Rolf Horn for helpful comments and discussions. This work is supported by Industry Canada, NSERC and CIFAR.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Institute for Quantum Computing and University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Dawei Lu, Aharon Brodutch, Jihyun Park, Hemant Katiyar, Tomas Jochym-O’Connor & Raymond Laflamme

  2. Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L 2Y5

    Raymond Laflamme

  3. Canadian Institute for Advanced Research, Toronto, ON, Canada, M5G 1Z8

    Raymond Laflamme

Authors
  1. Dawei Lu
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  2. Aharon Brodutch
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  3. Jihyun Park
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  4. Hemant Katiyar
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  5. Tomas Jochym-O’Connor
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  6. Raymond Laflamme
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Correspondence to Dawei Lu .

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Editors and Affiliations

  1. Department of Chemistry, Osaka City University Grad School Science, Osaka, Japan

    Takeji Takui

  2. Department of Chemistry and Biochemistry, University of Denver, Denver, Colorado, USA

    Lawrence Berliner

  3. Centre for Advanced Imaging, The University of Queensland, St. Lucia, Queensland, Australia

    Graeme Hanson

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Lu, D., Brodutch, A., Park, J., Katiyar, H., Jochym-O’Connor, T., Laflamme, R. (2016). NMR Quantum Information Processing. In: Takui, T., Berliner, L., Hanson, G. (eds) Electron Spin Resonance (ESR) Based Quantum Computing. Biological Magnetic Resonance, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3658-8_7

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