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Quantum bits are more robust to noise when they are encoded non-locally. Insuch an encoding, errors affecting the underlying physical system can then bedetected and corrected before they corrupt the encoded information. In 2001,Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance ofsuch a qubit, which is delocalised in the phase-space of a single oscillator.However, implementing measurements that reveal error syndromes of theoscillator while preserving the encoded information has proved experimentallychallenging: the only realisation so far relied on post-selection, which isincompatible with quantum error correction (QEC). The novelty of our experimentis precisely that it implements these non-destructive error-syndromemeasurements for a superconducting microwave cavity. We design and implement anoriginal feedback protocol that incorporates such measurements to preparesquare and hexagonal GKP code states. We then demonstrate QEC of an encodedqubit with unprecedented suppression of all logical errors, in quantitativeagreement with a theoretical estimate based on the measured imperfections ofthe experiment. Our protocol is applicable to other continuous variable systemsand, in contrast with previous implementations of QEC, can mitigate all logicalerrors generated by a wide variety of noise processes, and open a way towardsfault-tolerant quantum computation.

Quantum error correction of a qubit encoded in grid states of an oscillator