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arXiv:2206.03712 · Physical Review A

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

S. Nishio, Nicoló Lo Piparo, Michael Hanks, William J. Munro, Kae Nemoto

Published Mar 29, 2023• 3 citations

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-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 ($\mathrm{CX}$) gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of $\mathrm{CX}$ 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.

DOI: 10.1103/physreva.107.032620

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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 (

\mathrm{CX}

) gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of

\mathrm{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.

Distributed quantum information processing is based on the transmission of quantum data over lossy channels between quantum processing nodes. These nodes may be separated by a few microns or on planetary scale distances, but transmission losses due to absorption and/or scattering in the channel are the major source of error for most distributed quantum information tasks. Of course, quantum error correction (QEC) and detection techniques can be used to mitigate such effects, but error detection approaches have severe performance limitations due to the signaling constraints between nodes, and so error correction approaches are preferable-assuming one has sufficient high quality local operations. Typically, performance comparisons between loss-mitigating codes assume one encoded qubit per photon. However, single photons can carry more than one qubit of information and so our focus in this Letter is to explore whether loss-based QEC codes utilizing quantum multiplexed photons are viable and advantageous, especially as photon loss results in more than one qubit of information being lost. We show that quantum multiplexing enables significant resource reduction, in terms of the number of single-photon sources, while at the same time maintaining (or even lowering) the number of 2-qubit gates required. Further, our multiplexing approach requires only conventional optical gates already necessary for the implementation of these codes.

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