  In this paper, we place bounds on when it is impossible to purify a noisy
two-qubit state if all the gates used in the purification protocol are subject
to adversarial local, independent, noise. It is found that the gate operations
must be subject to less than 5.3% error. An existing proof that purification is
equivalent to error correction is used to show that this bound can also be
applied to concatenated error correcting codes in the presence of noisy gates,
and hence gives a limit to the tolerable error rate for a fault-tolerant
quantum computer formed by concatenation. This is shown to apply also to the
case where error detection and post-selection, as proposed by Knill, is used to
enhance the threshold. We demonstrate the trade-off between
gate/environmentally induced faulty rotations and qubit loss errors.
