  Bosonic codes offer noise resilience for quantum information processing. A
common type of noise in this setting is additive Gaussian noise, and a
long-standing open problem is to design a concatenated code that achieves the
hashing bound for this noise channel. Here we achieve this goal using a
Gottesman-Kitaev-Preskill (GKP) code to detect and discard error-prone qubits,
concatenated with a quantum parity code to handle the residual errors. Our
method employs a linear-time decoder and has applications in a wide range of
quantum computation and communication scenarios.
