Quantum error correction of a multimode grid code using confidence information, Part 2: Experiments

Bosonic codes leverage the large Hilbert space of harmonic oscillators to encode a qubit, thus leading to a more hardware-efficient approach to quantum computing. Notably, the single-mode grid code, known as the Gottesman-Kitaev-Preskill code [1], has been used to demonstrate experimentally quantum error correction (QEC) above break-even [2]. Here we implement, for the first time, state preparation and autonomous QEC of the two-mode tesseract grid code [3] in a superconducting dual-post cavity. The code performance as a quantum memory with autonomous QEC is compared with single-mode grid codes [4] implemented in the same hardware. Using the confidence information provided by mid-circuit measurements during the QEC process, we experimentally demonstrate that the logical error per round of QEC for the tesseract code scales more favorably with respect to the erasure probability compared to the single-mode grid code.



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

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

[3] B. Royer, S. Singh, and S. M. Girvin, PRX Quantum 3, 010335 (2022)

[4] D. Lachance-Quirion et al., Phys. Rev. Lett. 132, 150607 (2024)