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The unique features of quantum theory offer a powerful new paradigm forinformation processing. Translating these mathematical abstractions into usefulalgorithms and applications requires quantum systems with significantcomplexity and sufficiently low error rates. Such quantum systems must be madefrom robust hardware that can coherently store, process, and extract theencoded 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 quantumdevices. In particular, bosonic encodings in cQED that use multi-photon statesof superconducting cavities to encode information have shown success inrealizing hardware-efficient QEC. Here, we review recent developments in thetheory and implementation of quantum error correction with bosonic codes andreport the progress made towards realizing fault-tolerant quantum informationprocessing with cQED devices.

Quantum information processing with bosonic qubits in circuit QED