Small codes for magic state distillation

Abstract

Magic state distillation is a critical component in leading proposals for fault-tolerant quantum computation. Relatively little is known, however, about how to construct a magic state distillation routine or, more specifically, which stabilizer codes are suitable for the task. While transversality of a non-Clifford gate within a code often leads to efficient distillation routines, it appears to not be a necessary condition. Here we have examined a number of small stabilizer codes and highlight a handful of which displaying interesting, albeit inefficient, distillation behaviour. Many of these distill noisy states right up to the boundary of the known undististillable region, while some distill toward non-stabilizer states that have not previously been considered.

Graphical abstract

References

  1. 1.

    B. Eastin, E. Knill, Phys. Rev. Lett. 102, 110502 (2009)

    ADS  Article  Google Scholar 

  2. 2.

    E. Knill, Nature 434, 39 (2005)

    ADS  Article  Google Scholar 

  3. 3.

    S. Bravyi, A. Kitaev, Phys. Rev. A 71, 022316 (2005)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    H. Dawkins, M. Howard, Phys. Rev. Lett. 115, 030501 (2015)

    ADS  Article  Google Scholar 

  5. 5.

    H. Anwar, E.T. Campbell, D.E. Browne, New J. Phys. 14, 063006 (2012)

    ADS  Article  Google Scholar 

  6. 6.

    B.W. Reichardt, Quantum Inf. Comput. 9, 1030 (2009)

    MathSciNet  Google Scholar 

  7. 7.

    E.T. Campbell, D.E. Browne, Lect. Notes Comput. Sci. 5906, 20 (2009)

    MathSciNet  Article  Google Scholar 

  8. 8.

    A.M. Meier, B. Eastin, E. Knill, Quantum Inf. Commun. 13, 195 (2013)

    MathSciNet  Google Scholar 

  9. 9.

    S. Bravyi, J. Haah, Phys. Rev. A 86, 052329 (2012)

    ADS  Article  Google Scholar 

  10. 10.

    C. Jones, Phys. Rev. A 87, 042305 (2013)

    ADS  Article  Google Scholar 

  11. 11.

    E.T. Campbell, H. Anwar, D.E. Browne, Phys. Rev. X 2, 041021 (2012)

    Google Scholar 

  12. 12.

    A. Cross, G. Smith, J.A. Smolin, B. Zeng, Inf. Theory IEEE Trans. 55, 433 (2009)

    MathSciNet  Article  Google Scholar 

  13. 13.

    B.W. Reichardt, Quantum Inf. Process. 4, 251 (2005)

    MathSciNet  Article  Google Scholar 

  14. 14.

    E.T. Campbell, D.E. Browne, Phys. Rev. Lett. 104, 030503 (2010)

    ADS  Article  Google Scholar 

  15. 15.

    J.T. Anderson, T. Jochym-O’Connor, arXiv:1409.8320 (2014)

  16. 16.

    A. Bocharov, Y. Gurevich, K.M. Svore, Phys. Rev. A 88, 012313 (2013)

    ADS  Article  Google Scholar 

  17. 17.

    G. Duclos-Cianci, K. Svore, Phys. Rev. A 88, 042325 (2013)

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mark Howard.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Howard, M., Dawkins, H. Small codes for magic state distillation. Eur. Phys. J. D 70, 55 (2016). https://doi.org/10.1140/epjd/e2016-60682-y

Download citation

Keywords

  • Graph State
  • Bloch Sphere
  • Noise Rate
  • Bloch Vector
  • Stabilizer Code