  We present an encoded hybrid quantum repeater scheme using qubit-repetition
and Calderbank-Shor-Steane codes. For the case of repetition codes, we propose
an explicit implementation of the quantum error-correction protocol. Moreover,
we analyze the entangled-pair distribution rate for the hybrid quantum repeater
with encoding and we clearly identify a triple trade-off between the efficiency
of the codes, the memory decoherence time, and the local gate errors. Finally,
we show that in the presence of reasonable imperfections our system can achieve
rates of roughly 24 Hz per memory for 20 km repeater spacing, a final distance
of 1280 km, and a final fidelity of about 0.95.

Quantum Physics