  We compute the error threshold of color codes, a class of topological quantum
codes that allow a direct implementation of quantum Clifford gates, when both
qubit and measurement errors are present. By mapping the problem onto a
statistical-mechanical three-dimensional disordered Ising lattice gauge theory,
we estimate via large-scale Monte Carlo simulations that color codes are stable
against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson
loop distributions, we introduce a very sensitive probe to locate first-order
phase transitions in lattice gauge theories.
