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We introduce a new approach to Gottesman-Kitaev-Preskill (GKP) states thattreats their finite-energy version in an exact manner. Based on this analysis,we develop new qubit-oscillator circuits that autonomously stabilize a GKPmanifold, correcting errors without relying on qubit measurements. Finally, weshow numerically that logical information encoded in GKP states is very robustagainst typical oscillator noise sources when stabilized by these new circuits.

Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States