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We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction.
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Surface code quantum computing with error rates over 1 % 1\%
D. Wang, A. Fowler, and L. Hollenberg · 2011
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Surface codes: Towards practical large-scale quantum computation
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Strong resilience of topological codes to depolarization
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Optimal complexity correction of correlated errors in the surface code
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