Hardware-efficient quantum error correction via concatenated bosonic qubits.

To solve problems of practical importance, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches. Here, using a superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance d = 5 (ref.