  As there is no quantum error correction code with universal set of
transversal gates, several approaches have been proposed which, in combination
of transversal gates, make universal fault-tolerant quantum computation
possible. Magic state distillation, code switching, code concatenation and
pieceable fault-tolerance are well-known examples of such approaches. However,
the overhead of these approaches is one of the main bottlenecks for large-scale
quantum computation. In this paper, a hybrid approach is proposed which
combines the code concatenation technique with the other mentioned approaches.
The proposed approach outperforms code concatenation in terms of both number of
qubits and error threshold and also significantly reduces the resource overhead
of code switching, magic state distillation and pieceable fault-tolerance at
the cost of reducing the effective distance of the concatenated code for
implementing non-transversal gates.
