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

• URL: http://arxiv.org/abs/2206.03712v1
• Date: Wed, 8 Jun 2022 07:11:01 GMT
• Title: Resource Reduction in Multiplexed High-Dimensional Quantum Reed-Solomon Codes
• Authors: Shin Nishio, Nicol\`o Lo Piparo, Michael Hanks, William John Munro and Kae Nemoto
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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