  Gottesman-Kitaev-Preskill (GKP) states are a central resource for
fault-tolerant optical continuous-variable quantum computing and communication.
However, their realization in the optical domain remains to be demonstrated.
Here we propose a method for preparing GKP states using a cavity QED system as
the only non-Gaussian element. This system can be realized in several platforms
such as trapped atoms, quantum dots or diamond color centers. We simulate the
protocol with finite-cooperativity systems to evaluate the achievable quality
of the produced GKP states in realistic noisy systems. We further combine the
protocol with the previously proposed breeding protocol by Vasconcelos et al.
to relax the demands on the quality of the QED system. We find that GKP states
with more than 10 dB squeezing could be achieved in near-future experiments.
Additionally, the approach can be made fully deterministic, thus providing a
more scalable and hardware-efficient approach compared to probabilistic
approaches based on photon counting.
