  The highest current estimates for the amount of noise a quantum computer can
tolerate are based on fault-tolerance schemes relying heavily on postselecting
on no detected errors. However, there has been no proof that these schemes give
even a positive tolerable noise threshold. A technique to prove a positive
threshold, for probabilistic noise models, is presented. The main idea is to
maintain strong control over the distribution of errors in the quantum state at
all times. This distribution has correlations which conceivably could grow out
of control with postselection. But in fact, the error distribution can be
written as a mixture of nearby distributions each satisfying strong
independence properties, so there are no correlations for postselection to
amplify.
