Advertisement

Small codes for magic state distillation

  • Mark HowardEmail author
  • Hillary Dawkins
Open Access
Regular Article

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

Keywords

Graph State Bloch Sphere Noise Rate Bloch Vector Stabilizer Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    B. Eastin, E. Knill, Phys. Rev. Lett. 102, 110502 (2009)ADSCrossRefGoogle Scholar
  2. 2.
    E. Knill, Nature 434, 39 (2005)ADSCrossRefGoogle Scholar
  3. 3.
    S. Bravyi, A. Kitaev, Phys. Rev. A 71, 022316 (2005)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    H. Dawkins, M. Howard, Phys. Rev. Lett. 115, 030501 (2015)ADSCrossRefGoogle Scholar
  5. 5.
    H. Anwar, E.T. Campbell, D.E. Browne, New J. Phys. 14, 063006 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    B.W. Reichardt, Quantum Inf. Comput. 9, 1030 (2009)MathSciNetGoogle Scholar
  7. 7.
    E.T. Campbell, D.E. Browne, Lect. Notes Comput. Sci. 5906, 20 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    A.M. Meier, B. Eastin, E. Knill, Quantum Inf. Commun. 13, 195 (2013)MathSciNetGoogle Scholar
  9. 9.
    S. Bravyi, J. Haah, Phys. Rev. A 86, 052329 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    C. Jones, Phys. Rev. A 87, 042305 (2013)ADSCrossRefGoogle 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)MathSciNetCrossRefGoogle Scholar
  13. 13.
    B.W. Reichardt, Quantum Inf. Process. 4, 251 (2005)MathSciNetCrossRefGoogle Scholar
  14. 14.
    E.T. Campbell, D.E. Browne, Phys. Rev. Lett. 104, 030503 (2010)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  17. 17.
    G. Duclos-Cianci, K. Svore, Phys. Rev. A 88, 042325 (2013)ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Physics and Astronomy, University of SheffieldSheffieldUK
  2. 2.Institute for Quantum Computing and Department of Applied Mathematics, University of WaterlooWaterlooCanada
  3. 3.Institute for Quantum Computing and Department of Physics and Astronomy, University of WaterlooWaterlooCanada

Personalised recommendations