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Quantum Information and Computation     ISSN: 1533-7146      published since 2001
Vol.10 No.9&10  September 2010 

Graphical algorithms and threshold error rates for the 2d color code (pp0780-0802)
          
David S. Wang, Austin G. Fowler, Charles D. Hill, and Lloyd C.L. Hollenberg
         
doi: https://doi.org/10.26421/QIC10.9-10-5

Abstracts: Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1% [1, 2]. However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The color code of [3] is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the color code and its error correcting methodology, discussing one approximate technique based on graph matching. We derive an analytic lower bound to the threshold error rate of 6.25% under error-free syndrome extraction, while numerical simulations indicate it may be as high as 13.3%. Inclusion of faulty syndrome extraction circuits drops the threshold to approximately 0.10 ± 0.01%.
Key words: graphical algorithms, color code

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