Towards a second layer of quantum error correction for Gottesman-Kitaev-Preskill states

Approaches based on bosonic codes hold the promise of easing the requirements on the number of modes needed for fault-tolerant quantum computing compared with ones based on two-level systems. The finite-energy Gottesman-Kitaev-Preskill (GKP) code is of particular interest, as highlighted by recent experiments demonstrating an increase of its logical lifetime from quantum error correction (QEC) in superconducting devices [1-3]. Nevertheless, a second layer of quantum error correction will likely be required to reach the error rates necessary for useful quantum computation [4]. An important step in that direction is the demonstration of operations in an architecture involving multiple GKP qubits. Here, we present experimental progress on the implementation of a building block composed of a syndrome unit connected to two data units, each hosting an encoded GKP qubit.

[1] P. Campagne-Ibarcq et al.,Nature, 584, 368 (2019).

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

[3] D. Lachance-Quirion et al., arXiv:2310.11400 (2023).

[4] A. L. Grimsmo and S. Puri, PRX Quantum, 2, 020101 (2021).