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Generalized number-phase lattice encoding of a bosonic mode for quantum error correction

Author

Listed:
  • Dong-Long Hu

    (Sun Yat-sen University)

  • Weizhou Cai

    (University of Science and Technology of China)

  • Chang-Ling Zou

    (University of Science and Technology of China
    Hefei National Laboratory)

  • Ze-Liang Xiang

    (Sun Yat-sen University
    Sun Yat-sen University)

Abstract

Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in the quadrature phase space. Here we introduce a unified framework for encoding a qubit utilizing the symmetries in the phase space of number and phase variables of a bosonic mode. The logical codewords form lattice structures in the number-phase space, resulting in rectangular, oblique, and diamond-shaped lattice codes. Notably, oblique and diamond codes exhibit a number-phase vortex effect, where number-shift errors induce discrete phase rotations as syndromes, enabling efficient correction via phase measurements. These codes show significant performance advantages over conventional quadrature codes against dephasing noise in the potential one-way quantum communication applications. Our generalized number-phase codes open up new possibilities for fault-tolerant quantum computation and extending the quantum communication range with bosonic systems.

Suggested Citation

  • Dong-Long Hu & Weizhou Cai & Chang-Ling Zou & Ze-Liang Xiang, 2025. "Generalized number-phase lattice encoding of a bosonic mode for quantum error correction," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-62898-1
    DOI: 10.1038/s41467-025-62898-1
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