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Decoding color codes by projection onto surface codes
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We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect matching decoding algorithm for the three corresponding surface codes, we find a phase error threshold of approximately 8.7%. Finally, our approach enables us to establish a general lower bound on the error threshold of a family of color codes depending on the threshold of the three corresponding surface codes. These results are based on a chain complex interpretation of surface codes and color codes.
Forward citations
Cited by 2 Pith papers
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Planar fault-tolerant circuits for non-Clifford gates on the 2D color code
The paper constructs a family of planar fault-tolerant 'twisted color circuits' that implement logical T gates and magic-state measurements on the 2D color code via a path-integral and color-cohomology framework.
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Average-Case and Smoothed Near-Optimality for Color-Code Decoding
Block decoder for color codes yields (1+ε)-approx w.h.p. under i.i.d. and smoothed noise plus exact min-weight decoding in sparse low-p regime.
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