The unique features of quantum theory offer a powerful new paradigm for information processing. Translating these mathematical abstractions into useful algorithms and applications requires quantum systems with significant complexity and sufficiently low error rates. Such quantum systems must be made from robust hardware that can coherently store, process, and extract the encoded information, as well as possess effective quantum error correction (QEC) protocols to detect and correct errors. Circuit quantum electrodynamics (cQED) provides a promising hardware platform for implementing robust quantum devices. In particular, bosonic encodings in cQED that use multi-photon states of superconducting cavities to encode information have shown success in realizing hardware-efficient QEC. Here, we review recent developments in the theory and implementation of QEC with bosonic codes and report the progress made toward realizing fault-tolerant quantum information processing with cQED devices.

量子理论的独特特征为信息处理提供了强大的新范式。将这些数学抽象转化为有用的算法和应用程序需要具有显着复杂性和足够低错误率的量子系统。这样的量子系统必须由健壮的硬件组成，可以连贯地存储、处理和提取编码信息，并拥有有效的量子纠错 (QEC) 协议来检测和纠正错误。电路量子电动力学 (cQED) 为实现稳健的量子设备提供了一个有前途的硬件平台。特别是，cQED 中的玻色子编码使用超导腔的多光子状态来编码信息，在实现硬件高效 QEC 方面取得了成功。这里，