In this talk, we review recent experimental advances in GKP error-correction. We argue that propagation of errors from the ancillary mode employed in error-syndrome detection will hinder further progress with current schemes.

We propose two novel approaches to circumvent this roadblock. In the first approach, a buffer resonator mediates an effective coupling between a target mode hosting the GKP qubit and an ancillary two-level system. In this architecture, asymmetric preparation of the buffer in a GKP grid state robustly suppresses error-propagation. In the second approach, an ancillary mode directly couples to the target resonator via its GKP stabilizer operators, ensuring that no ancilla error may propagate at the logical level. We propose to engineer these exotic interactions in a high-impedance Josephson circuit driven with a microwave frequency comb, and to combine them with standard reservoir engineering techniques to enable continuous and autonomous error-correction of GKP qubits.

Finally, we show that Clifford gates on encoded GKP qubits may be applied while maintaining the continuous error-correction and preserving the finite-energy code structure, which should facilitate the assembly of GKP qubits in a robust quantum computing architecture.

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