Stabilization of finite-energy Gottesman-Kitaev-Preskill bosonic codes

Due to their large Hilbert space and their high quality factors, microwave cavities are an attractive candidate for the encoding of logical quantum information. One promising choice of encoding in these cavities is the Gottesman-Kitaev-Preskill (GKP) code which allows to protect against small displacements in phase space. However, in their ideal form, GKP codewords contain an infinite amount of energy and, consequently, their experimental implementation cannot be exact. Nevertheless, recent experiments [Flühmann et al., Nature (2019), Campagne-Ibarcq et al., arXiv:1907.12487] have demonstrated that it is possible to obtain long coherence times for GKP logical qubits. In this talk, we investigate improved stabilization strategies tailored specifically for finite-energy GKP codes and study how these protocols perform in a superconducting implementation with realistic parameters.