A Decoder for the Color Code with Boundaries

We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent to a boundary. We numerically estimate a threshold of $4% - 8%$forPauli$X$errorsandathresholdof$0.7% - 0.8%$forPauli$Z$ errors. Our work is a first step towards characterizing the performance of Bomb'{i}n’s recently proposed “colorful quantum computing.”