Advances and challenges in quantum error-correction with the Gottesman-Kitaev-Preskill code

Abstract:

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 oscillator 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 couples to the target oscillator via operators matching the GKP code stabilizers, ensuring that no ancilla error may propagate at the logical level. We propose to engineer such 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.