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Contextuality supplies the ‘magic’ for quantum computation

Nature volume 510, pages 351–355 (2014)Cite this article

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Abstract

Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple ‘hidden variable’ model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.

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Figure 1: A two-dimensional slice through qutrit state space.
Figure 2: Our construction applied to two qubits.

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Acknowledgements

M.H. was supported by the Irish Research Council (IRC) as part of the Empower Fellowship programme, and all authors acknowledge support from CIFAR and the Government of Canada through NSERC.

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Authors and Affiliations

  1. Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland

    Mark Howard

  2. Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada,

    Mark Howard, Joel Wallman, Victor Veitch & Joseph Emerson

  3. Department of Statistics, University of Toronto, 100 St George Street, Toronto, Ontario M5S 3G3, Canada,

    Victor Veitch

Authors
  1. Mark Howard
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  3. Victor Veitch
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  4. Joseph Emerson
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All authors made significant contributions to the results, interpretation and presentation of this Article.

Corresponding author

Correspondence to Joseph Emerson.

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The authors declare no competing financial interests.

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Howard, M., Wallman, J., Veitch, V. et al. Contextuality supplies the ‘magic’ for quantum computation. Nature 510, 351–355 (2014). https://doi.org/10.1038/nature13460

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