  We quantitatively analyze superradiance (collective emission) in a
three-dimensional array of qubits without imposing any restrictions on the size
of the sample. We show that even when the spacing between the qubits become
arbitrarily large, superradiance produces an error rate on each qubit that
scales with the total number of qubits. This is because the sum of the norms of
the effective Hamiltonians that decoheres each qubit scales with the total
number of qubits and is, therefore, unbounded. In three spatial dimensions, the
sum of the norms scales as $N^{2/3}$ where $N$ is the total number of qubits in
the computer. Because the sum of the Hamiltonian norms are unbounded, the
introduced errors are outside the applicability of the threshold theorem.
