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Efficient color code decoders in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>2</mml:mn></mml:math> dimensions from toric code decoders
We introduce an efficient decoder of the color code in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>2</mml:mn></mml:math> dimensions, the Restriction Decoder, which uses any <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and …