Fault-tolerant state preparation of GKP states
There have been several recent results regarding Gottesman-Kitaev-Preskill (GKP) codes which have generated a lot of interest. For one, a new decoding algorithm has shown how GKP codes can be used with the surface code to obtain higher thresholds. It has also been shown how, given a supply of input GKP encoded states, Gaussian operations are sufficient for universal quantum computation. The above motivates the need for having rigorous fault-tolerant methods for preparing GKP states. In this talk I will first provide clear definitions for the fault-tolerant state preparation of a GKP state. I will then show how the phase estimation protocol in can changed to fault-tolerantly prepare an encoded GKP state. Using analytically derived expressions for the time evolution due to the Kerr non-linearity, I will show how our methods can be used in circuit QED to fault-tolerantly prepare GKP states.