  We study quasi-exact quantum error correcting codes and quantum computation
with them. A quasi-exact code is an approximate code such that it contains a
finite number of scaling parameters, the tuning of which can flow it to
corresponding exact codes, serving as its fixed points. The computation with a
quasi-exact code cannot realize any logical gate to arbitrary accuracy. To
overcome this, the notion of quasi-exact universality is proposed, which makes
quasi-exact quantum computation a feasible model especially for executing
moderate-size algorithms. We find that the incompatibility between universality
and transversality of the set of logical gates does not persist in the
quasi-exact scenario. A class of covariant quasi-exact codes is defined which
proves to support transversal and quasi-exact universal set of logical gates
for $SU(d)$. This work opens the possibility of quantum computation with
quasi-exact universality, transversality, and fault tolerance.
