Resource Reduction in Multiplexed High-Dimensional Quantum Reed-Solomon Codes

TL;DR

This paper introduces a quantum multiplexing technique to reduce resource requirements in high-dimensional quantum Reed-Solomon codes, making quantum error correction more practical for communication systems.

Contribution

It proposes a method to decompose multi-controlled gates with fewer CX gates using quantum multiplexing, applicable to various quantum codes and algorithms.

Findings

Significant reduction in CX gates for encoding circuits.

Method applicable to multiple quantum error correction codes.

Potential to improve practicality of quantum communication systems.

Abstract

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 correction codes are one important technique to address this issue. In particular, the Quantum Reed-Solomon codes are known to be quite efficient for quantum communication tasks. 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 multi-controlled gates using fewer $\rm{CX}$ gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of $\rm{CX}$ gates needed in the encoding circuits for the quantum Reed-Solomon code. Our approach is also applicable to many other quantum error correction codes and quantum algorithms, including Grovers and quantum walks.