  We analyze the problem of a quantum computer in a correlated environment
protected from decoherence by QEC using a perturbative renormalization group
approach. The scaling equation obtained reflects the competition between the
dimension of the computer and the scaling dimension of the correlations. For an
irrelevant flow, the error probability is reduced to a stochastic form for long
time and/or large number of qubits; thus, the traditional derivation of the
threshold theorem holds for these error models. In this way, the ``threshold
theorem'' of quantum computing is rephrased as a dimensional criterion.
