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Abstract

A method for correcting a color code over a quantum erasure channel. First, a forest spanning the erased qubits over the lattice defining the color code is determined and syndrome qubits are calculated for each face of the tiling. If none of the faces of the tiling is touched by more than one tree, the erased qubits of each tree are sequentially decoded according to a trimming process. If a face of the tiling is touched by different trees, pseudo-erasures can be first inserted in order to connect these trees and the extended forest is subjected to the trimming process. Where a face of the tiling touched by a leaf is also touched by another vertex of the forest, the vertex belonging to this face and to the forest can be inactivated, and when the trimming process is terminated, a linear system with variables associated by the inactivated vertices of the forest is solved.

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First Claim