Resource reduction in multiplexed high-dimensional quantum Reed-Solomon codes

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.