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Quantum error correction of qudits beyond break-even

Author

Listed:
  • Benjamin L. Brock

    (Yale University
    Yale University
    Yale University)

  • Shraddha Singh

    (Yale University
    Yale University
    Yale University)

  • Alec Eickbusch

    (Yale University
    Yale University
    Yale University
    Google Quantum AI)

  • Volodymyr V. Sivak

    (Yale University
    Yale University
    Yale University
    Google Quantum AI)

  • Andy Z. Ding

    (Yale University
    Yale University
    Yale University)

  • Luigi Frunzio

    (Yale University
    Yale University
    Yale University)

  • Steven M. Girvin

    (Yale University
    Yale University
    Yale University)

  • Michel H. Devoret

    (Yale University
    Yale University
    Yale University
    UC Santa Barbara Department of Physics and Google Quantum AI)

Abstract

Hilbert space dimension is a key resource for quantum information processing1,2. Not only is a large overall Hilbert space an essential requirement for quantum error correction, but a large local Hilbert space can also be advantageous for realizing gates and algorithms more efficiently3–7. As a result, there has been considerable experimental effort in recent years to develop quantum computing platforms using qudits (d-dimensional quantum systems with d > 2) as the fundamental unit of quantum information8–19. Just as with qubits, quantum error correction of these qudits will be necessary in the long run, but so far, error correction of logical qudits has not been demonstrated experimentally. Here we report the experimental realization of an error-corrected logical qutrit (d = 3) and ququart (d = 4), which was achieved with the Gottesman–Kitaev–Preskill bosonic code20. Using a reinforcement learning agent21,22, we optimized the Gottesman–Kitaev–Preskill qutrit (ququart) as a ternary (quaternary) quantum memory and achieved beyond break-even error correction with a gain of 1.82 ± 0.03 (1.87 ± 0.03). This work represents a novel way of leveraging the large Hilbert space of a harmonic oscillator to realize hardware-efficient quantum error correction.

Suggested Citation

  • Benjamin L. Brock & Shraddha Singh & Alec Eickbusch & Volodymyr V. Sivak & Andy Z. Ding & Luigi Frunzio & Steven M. Girvin & Michel H. Devoret, 2025. "Quantum error correction of qudits beyond break-even," Nature, Nature, vol. 641(8063), pages 612-618, May.
  • Handle: RePEc:nat:nature:v:641:y:2025:i:8063:d:10.1038_s41586-025-08899-y
    DOI: 10.1038/s41586-025-08899-y
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