Skip to main content

Practical quantum fault tolerance

Publication ,  Journal Article
Gilbert, G; Weinstein, YS; Aggarwal, V; Calderbank, AR
Published in: Proceedings of SPIE - The International Society for Optical Engineering
September 10, 2009

The standard approach to quantum fault tolerance is to calculate error thresholds on basic gates in the limit of arbitrarily many concatenation levels. In contrast this paper takes the number of qubits and the target implementation accuracy as given, and provides a framework for engineering the constrained quantum system to the required tolerance. The approach requires solving the full dynamics of the quantum system for an arbitrary admixture (biased or unbiased) of Pauli errors. The inaccuracy between ideal and implemented quantum systems is captured by the supremum of the Schatten k-norm of the difference between the ideal and implemented density matrices taken over all density matrices. This is a more complete analysis than the standard approach, where an intricate combination of worst case assumptions and combinatorial analysis is used to analyze the special case of equiprobable errors. Conditions for fault tolerance are now expressed in terms of error regions rather than a single number (the standard error threshold). In the important special case of a stochastic noise model and a single logical qubit, an optimization over all 2×2 density matrices is required to obtain the full dynamics. The complexity of this calculation is greatly simplified through reduction to an optimization over only three projectors. Error regions are calculated for the standard 5- and 7-qubit codes. Knowledge of the full dynamics makes it possible to design sophisticated concatenation strategies that go beyond repeatedly using the same code, and these strategies can achieve target fault tolerance thresholds with fewer qubits. © 2009 SPIE.

Duke Scholars

Published In

Proceedings of SPIE - The International Society for Optical Engineering

DOI

ISSN

0277-786X

Publication Date

September 10, 2009

Volume

7342

Related Subject Headings

  • 5102 Atomic, molecular and optical physics
  • 4009 Electronics, sensors and digital hardware
  • 4006 Communications engineering
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Gilbert, G., Weinstein, Y. S., Aggarwal, V., & Calderbank, A. R. (2009). Practical quantum fault tolerance. Proceedings of SPIE - The International Society for Optical Engineering, 7342. https://doi.org/10.1117/12.818683
Gilbert, G., Y. S. Weinstein, V. Aggarwal, and A. R. Calderbank. “Practical quantum fault tolerance.” Proceedings of SPIE - The International Society for Optical Engineering 7342 (September 10, 2009). https://doi.org/10.1117/12.818683.
Gilbert G, Weinstein YS, Aggarwal V, Calderbank AR. Practical quantum fault tolerance. Proceedings of SPIE - The International Society for Optical Engineering. 2009 Sep 10;7342.
Gilbert, G., et al. “Practical quantum fault tolerance.” Proceedings of SPIE - The International Society for Optical Engineering, vol. 7342, Sept. 2009. Scopus, doi:10.1117/12.818683.
Gilbert G, Weinstein YS, Aggarwal V, Calderbank AR. Practical quantum fault tolerance. Proceedings of SPIE - The International Society for Optical Engineering. 2009 Sep 10;7342.

Published In

Proceedings of SPIE - The International Society for Optical Engineering

DOI

ISSN

0277-786X

Publication Date

September 10, 2009

Volume

7342

Related Subject Headings

  • 5102 Atomic, molecular and optical physics
  • 4009 Electronics, sensors and digital hardware
  • 4006 Communications engineering