The quantum noise threshold is the maximum tolerable gate error rate
allowing reliable quantum computation. The noise threshold (and how
it trades off versus overhead) roughly determines how hard it is to
build a useful quantum computer.

The highest current estimates for the noise threshold are based on
fault-tolerance schemes relying heavily on postselection -- error
detection instead of error correction. However, it was not known if
these schemes had any positive threshold at all. The problem is that
correlations in the distribution of errors in the system can, a
priori, quickly grow out of control, stymying proofs. In fact,
though, correlations can be shown to decay by maintaining a strong
inductive assumption: the error distribution can be written as a
mixture of nearby distributions in which errors occur independently.