Quantum Error Correction of Qudits Beyond Break-even

Hilbert space dimension is a key resource for quantum information processing. Crucially, quantum error correction requires a large overall Hilbert space to redundantly encode quantum information, but access to a large local Hilbert space can also be advantageous for realizing gates and algorithms more efficiently. There has thus 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. Just as with qubits, quantum error correction of these qudits will be necessary in the long run, but to date 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) by employing the Gottesman-Kitaev-Preskill (GKP) bosonic code [1]. Using a reinforcement learning agent [2], we optimize the GKP qutrit (ququart) as a ternary (quaternary) quantum memory and achieve beyond break-even error correction with a gain of 1.82 +/- 0.03 (1.87 +/- 0.03). This work [3] represents a new way of leveraging the large Hilbert space of a harmonic oscillator for hardware-efficient quantum error correction.

[1] Gottesman, Kitaev, and Preskill, Phys. Rev. A 64, 012310 (2001).

[2] Sivak et al., Nature 616, 50-55 (2023).

[3] Brock et al., arXiv:2409.15065 (2024).