  We show that quantum Reed-Solomon codes constructed from classical
Reed-Solomon codes can approach the capacity on the quantum erasure channel of
$d$-level systems for large dimension $d$. We study the performance of one-way
quantum repeaters with these codes and obtain a significant improvement in key
generation rate compared to previously investigated encoding schemes with
quantum parity codes and quantum polynomial codes. We also compare the three
generation of quantum repeaters using quantum Reed-Solomon codes and identify
parameter regimes where each generation performs the best.
