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Quantum information is vulnerable to environmental noise and experimentalimperfections, hindering the reliability of practical quantum informationprocessors. Therefore, quantum error correction (QEC) that can protect quantuminformation against noise is vital for universal and scalable quantumcomputation. Among many different experimental platforms, superconductingquantum circuits and bosonic encodings in superconducting microwave modes areappealing for their unprecedented potential in QEC. During the last few years,bosonic QEC is demonstrated to reach the break-even point, i.e. the lifetime ofa logical qubit is enhanced to exceed that of any individual componentscomposing the experimental system. Beyond that, universal gate sets andfault-tolerant operations on the bosonic codes are also realized, pushingquantum information processing towards the QEC era. In this article, we reviewthe recent progress of the bosonic codes, including theGottesman-Kitaev-Preskill codes, cat codes, and binomial codes, and discuss theopportunities of bosonic codes in various quantum applications, ranging fromfault-tolerant quantum computation to quantum metrology. We also summarize thechallenges associated with the bosonic codes and provide an outlook for thepotential research directions in the long terms.

Bosonic quantum error correction codes in superconducting quantum circuits