  We prove an accuracy threshold theorem for fault-tolerant quantum computation
based on error detection and postselection. Our proof provides a rigorous
foundation for the scheme suggested by Knill, in which preparation circuits for
ancilla states are protected by a concatenated error-detecting code and the
preparation is aborted if an error is detected. The proof applies to
independent stochastic noise but (in contrast to proofs of the quantum accuracy
threshold theorem based on concatenated error-correcting codes) not to
strongly-correlated adversarial noise. Our rigorously established lower bound
on the accuracy threshold, 1.04 \times 10^{-3}, is well below Knill's numerical
estimates.
