  For a simple model of mutually interacting qubits it is shown how the errors
induced by mutual interactions can be eliminated using concatenated coding. The
model is solved exactly for arbitrary interaction strength, for two well-known
codes, one and two levels deep: this allows one to see under which
circumstances error amplitudes add coherently or incoherently. For deeper
concatenation, approximate results are derived which make it possible to
calculate an approximate ``threshold'' value for the product of interaction
strength and free evolution time, below which the failure probability for an
encoded qubit decreases exponentially with the depth of the encoding. The
results suggest that concatenated coding could fully handle the errors arising
from mutual interactions, at no extra cost, in terms of resources needed, from
what would be required to deal with random environmental errors.
