Graphical algorithms and threshold error rates for the 2d colour code

Details Graphical algorithms and threshold error rates for the 2d colour code Graphical algorithms and threshold error rates for the 2d colour code

2009-07-10

arxiv.org/abs/0907.1708v1

Quantum Information and Computation 10, 780 (2010)

Physics

Quantum Physics

20 pages, 19 figures

Scientific paper

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% (NJoP 9:199, 2007), (arXiv:0905.0531). However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The colour code of (PRL 97:180501, 2006) is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the colour 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 0.1%.

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