We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random 3-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p_c = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities does not necessarily imply lower resistance to noise.
@article{arxiv.0902.4845,
title = {Error Threshold for Color Codes and Random 3-Body Ising Models},
author = {Helmut G. Katzgraber and H. Bombin and M. A. Martin-Delgado},
journal= {arXiv preprint arXiv:0902.4845},
year = {2009}
}