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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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    as
    1. Laird Egan & Dripto M. Debroy & Crystal Noel & Andrew Risinger & Daiwei Zhu & Debopriyo Biswas & Michael Newman & Muyuan Li & Kenneth R. Brown & Marko Cetina & Christopher Monroe, 2021. "Fault-tolerant control of an error-corrected qubit," Nature, Nature, vol. 598(7880), pages 281-286, October.
    2. Alexei Ourjoumtsev & Hyunseok Jeong & Rosa Tualle-Brouri & Philippe Grangier, 2007. "Generation of optical ‘Schrödinger cats’ from photon number states," Nature, Nature, vol. 448(7155), pages 784-786, August.
    3. M. H. Abobeih & Y. Wang & J. Randall & S. J. H. Loenen & C. E. Bradley & M. Markham & D. J. Twitchen & B. M. Terhal & T. H. Taminiau, 2022. "Fault-tolerant operation of a logical qubit in a diamond quantum processor," Nature, Nature, vol. 606(7916), pages 884-889, June.
    4. V. V. Sivak & A. Eickbusch & B. Royer & S. Singh & I. Tsioutsios & S. Ganjam & A. Miano & B. L. Brock & A. Z. Ding & L. Frunzio & S. M. Girvin & R. J. Schoelkopf & M. H. Devoret, 2023. "Real-time quantum error correction beyond break-even," Nature, Nature, vol. 616(7955), pages 50-55, April.
    5. Masahiro Takeoka & Saikat Guha & Mark M. Wilde, 2014. "Fundamental rate-loss tradeoff for optical quantum key distribution," Nature Communications, Nature, vol. 5(1), pages 1-7, December.
    6. E. Knill, 2005. "Quantum computing with realistically noisy devices," Nature, Nature, vol. 434(7029), pages 39-44, March.
    7. Shakib Daryanoosh & Sergei Slussarenko & Dominic W. Berry & Howard M. Wiseman & Geoff J. Pryde, 2018. "Experimental optical phase measurement approaching the exact Heisenberg limit," Nature Communications, Nature, vol. 9(1), pages 1-6, December.
    8. Kenta Takeda & Akito Noiri & Takashi Nakajima & Takashi Kobayashi & Seigo Tarucha, 2022. "Quantum error correction with silicon spin qubits," Nature, Nature, vol. 608(7924), pages 682-686, August.
    9. Xing-Can Yao & Tian-Xiong Wang & Hao-Ze Chen & Wei-Bo Gao & Austin G. Fowler & Robert Raussendorf & Zeng-Bing Chen & Nai-Le Liu & Chao-Yang Lu & You-Jin Deng & Yu-Ao Chen & Jian-Wei Pan, 2012. "Experimental demonstration of topological error correction," Nature, Nature, vol. 482(7386), pages 489-494, February.
    10. G. Waldherr & Y. Wang & S. Zaiser & M. Jamali & T. Schulte-Herbrüggen & H. Abe & T. Ohshima & J. Isoya & J. F. Du & P. Neumann & J. Wrachtrup, 2014. "Quantum error correction in a solid-state hybrid spin register," Nature, Nature, vol. 506(7487), pages 204-207, February.
    11. Zhongchu Ni & Sai Li & Xiaowei Deng & Yanyan Cai & Libo Zhang & Weiting Wang & Zhen-Biao Yang & Haifeng Yu & Fei Yan & Song Liu & Chang-Ling Zou & Luyan Sun & Shi-Biao Zheng & Yuan Xu & Dapeng Yu, 2023. "Beating the break-even point with a discrete-variable-encoded logical qubit," Nature, Nature, vol. 616(7955), pages 56-60, April.
    12. Nissim Ofek & Andrei Petrenko & Reinier Heeres & Philip Reinhold & Zaki Leghtas & Brian Vlastakis & Yehan Liu & Luigi Frunzio & S. M. Girvin & L. Jiang & Mazyar Mirrahimi & M. H. Devoret & R. J. Schoe, 2016. "Extending the lifetime of a quantum bit with error correction in superconducting circuits," Nature, Nature, vol. 536(7617), pages 441-445, August.
    13. B. L. Higgins & D. W. Berry & S. D. Bartlett & H. M. Wiseman & G. J. Pryde, 2007. "Entanglement-free Heisenberg-limited phase estimation," Nature, Nature, vol. 450(7168), pages 393-396, November.
    14. J. Kelly & R. Barends & A. G. Fowler & A. Megrant & E. Jeffrey & T. C. White & D. Sank & J. Y. Mutus & B. Campbell & Yu Chen & Z. Chen & B. Chiaro & A. Dunsworth & I.-C. Hoi & C. Neill & P. J. J. O’Ma, 2015. "State preservation by repetitive error detection in a superconducting quantum circuit," Nature, Nature, vol. 519(7541), pages 66-69, March.
    15. Sebastian Krinner & Nathan Lacroix & Ants Remm & Agustin Paolo & Elie Genois & Catherine Leroux & Christoph Hellings & Stefania Lazar & Francois Swiadek & Johannes Herrmann & Graham J. Norris & Christ, 2022. "Realizing repeated quantum error correction in a distance-three surface code," Nature, Nature, vol. 605(7911), pages 669-674, May.
    16. X. L. He & Yong Lu & D. Q. Bao & Hang Xue & W. B. Jiang & Z. Wang & A. F. Roudsari & Per Delsing & J. S. Tsai & Z. R. Lin, 2023. "Fast generation of Schrödinger cat states using a Kerr-tunable superconducting resonator," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    17. Lukas Postler & Sascha Heuβen & Ivan Pogorelov & Manuel Rispler & Thomas Feldker & Michael Meth & Christian D. Marciniak & Roman Stricker & Martin Ringbauer & Rainer Blatt & Philipp Schindler & Markus, 2022. "Demonstration of fault-tolerant universal quantum gate operations," Nature, Nature, vol. 605(7911), pages 675-680, May.
    18. J. Chiaverini & D. Leibfried & T. Schaetz & M. D. Barrett & R. B. Blakestad & J. Britton & W. M. Itano & J. D. Jost & E. Knill & C. Langer & R. Ozeri & D. J. Wineland, 2004. "Realization of quantum error correction," Nature, Nature, vol. 432(7017), pages 602-605, December.
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