  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.
