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 generations of quantum repeaters using quantum Reed-Solomon codes and identify parameter regimes where each generation performs the best.
Quantum communication technologies will play an important role in quantum information processing in the near future as we network devices together. However, their implementation is still a challenging task due to both loss and gate errors. Quantum error-correcting codes are one important technique to address this issue. In particular, the quantum Reed-Solomon codes well suited to communication tasks as photons can naturally carry more than one qubit of information. The high degree of physical resources required, however, makes such a code difficult to use in practice. A recent technique called quantum multiplexing has been shown to reduce resources by using multiple degrees of freedom of a photon. In this work, we propose a method to decompose multicontrolled gates using fewer controlled-x (
CX) gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of
CX gates needed in the encoding circuits for the quantum Reed-Solomon code. Our approach is also applicable to many other quantum error-correcting codes and quantum algorithms, including Grovers and quantum walks.