  A family of quantum codes of increasing block length with positive rate is
asymptotically good if the ratio of its distance to its block length approaches
a positive constant. The asymptotic quantum Gilbert-Varshamov (GV) bound states
that there exist $q$-ary quantum codes of sufficiently long block length $N$
having fixed rate $R$ with distance at least $N H^{-1}_{q^2}((1-R)/2)$, where
$H_{q^2}$ is the $q^2$-ary entropy function. For $q < 7$, only random quantum
codes are known to asymptotically attain the quantum GV bound. However, random
codes have little structure. In this paper, we generalize the classical result
of Thommesen to the quantum case, thereby demonstrating the existence of
concatenated quantum codes that can asymptotically attain the quantum GV bound.
The outer codes are quantum generalized Reed-Solomon codes, and the inner codes
are random independently chosen stabilizer codes, where the rates of the inner
and outer codes lie in a specified feasible region.
