Autonomous Quantum Error Correction of Multi-mode Qunaught-Assisted GKP Code

Bosonic codes, in which quantum error corrected qubits are encoded into complex states of light, are promising candidates to implement hardware efficient quantum processors. Circuit quantum electrodynamics architectures enables these codes to be implemented in the inherently large Hilbert space of a microwave cavity. In these architectures, grid states such as single-mode Gottesman-Kitaev-Preskill (GKP) states have demonstrated great performance, where lifetime has been improved beyond break-even [1]. Additionally, going from single-mode to multi-mode grid states can increase the robustness to error propagation from auxiliary qubits used for quantum error correction [2].

In this work, we propose and realize a new multi-mode encoding, the Qunaught-Assisted GKP. Here, the logical information is encoded in a single-mode GKP code, while a qunaught grid state in an additional mode acts as a flag for errors. We implement it experimentally in a 3D double-post cavity coupled to an auxiliary transmon. We compare the performance of the single mode square GKP and the Qunaught-Assisted GKP during autonomous quantum error correction [3] using sBs stabilization protocol [4-5].

1. V. V. Sivak et al., Nature 616, 50-55 (2023)

2. B. Royer et al., PRX Quantum 3, 010335 (2022)

3. D. Lachance-Quirion, Phys. Rev. Lett. 132, 150607 (2024)

3. B. Royer et al., Phys. Rev. Lett. 125, 260509 (2020)

4. B. de Neeve et al., Nat. Phys. 18, 296-300 (2022)