  We establish and explore a new connection between quantum information theory
and classical statistical mechanics by studying the problem of qubit losses in
2D topological color codes. We introduce a protocol to cope with qubit losses,
which is based on the identification and removal of a twin qubit from the code,
and which guarantees the recovery of a valid three-colorable and trivalent
reconstructed color code lattice. Moreover, we show that determining the
corresponding qubit loss error threshold is equivalent to a new generalized
classical percolation process. We numerically compute the associated qubit loss
thresholds for two families of 2D color code and find that these are close to
satisfying the fundamental limit $p_\text{fund} = 0.461 \pm 0.005$ close to the
50% as imposed by the no-cloning theorem. Our findings reveal a new connection
between topological color codes and percolation theory, show high robustness of
color codes against qubit loss, and are relevant for implementations of quantum
error correction in various physical platforms.
