  A promising approach to overcome decoherence in quantum computing schemes is
to perform active quantum error correction using topology. Topological
subsystem codes incorporate both the benefits of topological and subsystem
codes, allowing for error syndrome recovery with only 2-local measurements in a
two-dimensional array of qubits. We study the error threshold for topological
subsystem color codes under very general external noise conditions. By
transforming the problem into a classical disordered spin model, we estimate
using Monte Carlo simulations that topological subsystem codes have an optimal
error tolerance of 5.5(2)%. This means there is ample space for improvement in
existing error-correcting algorithms that typically find a threshold of
approximately 2%.
