Real-time quantum error correction beyond break-even.

The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process1-7 faced the generation of an excessive number of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. Here we answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is substantially longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G = 2.27 ± 0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.

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

The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. One method to achieve this is quantum error correction (QEC), which prevents noise in the underlying system from causing logical errors. This approach derives from the reasonable assumption that noise is local, that is, it does not act in a coordinated way on different parts of the physical system. Therefore, if a logical qubit is encoded non-locally, we can-for a limited time-detect and correct noise-induced evolution before it corrupts the encoded information1. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a non-local qubit: a superposition of position eigenstates that forms grid states of a single oscillator2. However, the implementation of measurements that reveal this noise-induced evolution of the oscillator while preserving the encoded information3-7 has proved to be experimentally challenging, and the only realization reported so far relied on post-selection8,9, which is incompatible with QEC. Here we experimentally prepare square and hexagonal GKP code states through a feedback protocol that incorporates non-destructive measurements that are implemented with a superconducting microwave cavity having the role of the oscillator. We demonstrate QEC of an encoded qubit with suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous-variable systems and, in contrast to previous implementations of QEC10-14, can mitigate all logical errors generated by a wide variety of noise processes and facilitate fault-tolerant quantum computation.