Control, gates, and error correction of GKP codes in bosonic cQED

The past four years have seen rapid experimental progress in realizing the bosonic quantum error correction code proposed in 2001 by Gottesman, Kitaev, and Preskill (GKP), in which logical states are encoded as grid states of an oscillator [1]. Recent experimental milestones include the preparation and real-time error correction of the GKP code in trapped-ion and circuit quantum electrodynamics (cQED) architectures [2-6]. In this talk, I will review the bosonic cQED experiments that have led to some of these recent advances, focusing on the engineering of tools needed for error correction of the GKP code [2] and how the same tools can be used for universal control of an oscillator with weak dispersive coupling to a qubit [5]. I will also discuss our recent results on optimizing the error correction protocol using model-free reinforcement learning, leading to the demonstration of a fully error-corrected quantum memory with coherence beyond break even [6]. Finally, I will discuss our ongoing experimental work towards realizing single- and two-qubit gates on error-corrected GKP qubits.

[1] Gottesman, Kitaev, Preskill, PRA 2001; [2] Campagne-Ibarcq, Eickbusch, Touzard et al. Nature 2020 ; [3] Flühmann et al. Nature 2019 ; [4] de Neeve et al. Nature Physics 2022; [5] Eickbusch et al. Nature Physics 2022; [6] Sivak et al. in preparation 2022.