  We investigate the usage of highly efficient error correcting codes of
multilevel systems to protect encoded quantum information from erasure errors
and implementation to repetitively correct these errors. Our scheme makes use
of quantum polynomial codes to encode quantum information and generalizes
teleportation based error correction for multilevel systems to correct photon
losses and operation errors in a fault-tolerant manner. We discuss the
application of quantum polynomial codes to one-way quantum repeaters. For
various types of operation errors, we identify different parameter regions
where quantum polynomial codes can achieve a superior performance compared to
qubit based quantum parity codes.
