Quantum error correction of qudits beyond break-even

Benjamin L Brock; Shraddha Singh; Alec Eickbusch; Volodymyr V Sivak; Andy Z Ding; Luigi Frunzio; Steven M Girvin; Michel H Devoret

doi:10.1038/s41586-025-08899-y

Quantum error correction of qudits beyond break-even

Nature. 2025 May;641(8063):612-618. doi: 10.1038/s41586-025-08899-y. Epub 2025 May 14.

Authors

Benjamin L Brock^{1

2

3}, Shraddha Singh^{4

5

6}, Alec Eickbusch^{4

5

6

7}, Volodymyr V Sivak^{4

5

6

7}, Andy Z Ding^{4

5

6}, Luigi Frunzio^{4

5

6}, Steven M Girvin^{4

5

6}, Michel H Devoret^{8

9

10

11}

Affiliations

¹ Department of Applied Physics, Yale University, New Haven, CT, USA. benjamin.brock@yale.edu.
² Yale Quantum Institute, Yale University, New Haven, CT, USA. benjamin.brock@yale.edu.
³ Department of Physics, Yale University, New Haven, CT, USA. benjamin.brock@yale.edu.
⁴ Department of Applied Physics, Yale University, New Haven, CT, USA.
⁵ Yale Quantum Institute, Yale University, New Haven, CT, USA.
⁶ Department of Physics, Yale University, New Haven, CT, USA.
⁷ Google Quantum AI, Santa Barbara, CA, USA.
⁸ Department of Applied Physics, Yale University, New Haven, CT, USA. michel.devoret@yale.edu.
⁹ Yale Quantum Institute, Yale University, New Haven, CT, USA. michel.devoret@yale.edu.
¹⁰ Department of Physics, Yale University, New Haven, CT, USA. michel.devoret@yale.edu.
¹¹ UC Santa Barbara Department of Physics and Google Quantum AI, Santa Barbara, CA, USA. michel.devoret@yale.edu.

Abstract

Hilbert space dimension is a key resource for quantum information processing^1,2. 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 efficiently^3-7. 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 information^8-19. 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 agent^21,22, 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.