  Consider a 2-D square array of qubits of extent $L\times L$. We provide a
proof that the minimum weight perfect matching problem associated with running
a particular class of topological quantum error correction codes on this array
can be exactly solved with a 2-D square array of classical computing devices,
each of which is nominally associated with a fixed number $N$ of qubits, in
constant average time per round of error detection independent of $L$ provided
physical error rates are below fixed nonzero values, and other physically
reasonable assumptions. This proof is applicable to the fully fault-tolerant
case only, not the case of perfect stabilizer measurements.
