  We prove a new version of the quantum threshold theorem that applies to
concatenation of a quantum code that corrects only one error, and we use this
theorem to derive a rigorous lower bound on the quantum accuracy threshold
epsilon_0. Our proof also applies to concatenation of higher-distance codes,
and to noise models that allow faults to be correlated in space and in time.
The proof uses new criteria for assessing the accuracy of fault-tolerant
circuits, which are particularly conducive to the inductive analysis of
recursive simulations. Our lower bound on the threshold, epsilon_0 > 2.73
\times 10^{-5} for an adversarial independent stochastic noise model, is
derived from a computer-assisted combinatorial analysis; it is the best lower
bound that has been rigorously proven so far.
