  We study how the resilience of the surface code is affected by the coupling
to a non-Markovian environment at zero temperature. The qubits in the surface
code experience an effective dynamics due to the coupling to the environment
that induces correlations among them. The range of the effective induced
qubit-qubit interaction depends on parameters related to the environment and
the duration of the quantum error correction cycle. We show numerically that
different interaction ranges set different intrinsic bounds on the fidelity of
the code. These bounds are unrelated to the error thresholds based on
stochastic error models. We introduce a definition of stabilizers based on
logical operators that allows us to efficiently implement a Metropolis
algorithm to determine upper bounds to the fidelity error threshold.
