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% for Pauli X errors and a threshold of 0.7%−0.8% for Pauli Z errors. Our work is a first step towards characterizing the performance of Bomb\'{i}n's recently proposed "colorful quantum computing."
@article{arxiv.2003.11602,
title = {A Decoder for the Color Code with Boundaries},
author = {Skylar Turner and Josey Hanish and Eion Blanchard and Noah Davis and Brian La Cour},
journal= {arXiv preprint arXiv:2003.11602},
year = {2021}
}