Tutorial on Bosonic Codes
summary
Survey of bosonic codes compares specific code families, noise models and lab results: GKP lattice codes (phase-space lattices, displacement/nullifier formalism) protect against small shifts and surprisingly outperform cat/binomial codes under photon loss; cat codes with Lindblad stabilization (two‑ and four‑component cats) realize continuous CNOTs and enable the first beyond‑break‑even microwave experiments; binomial/Fock and number–phase codes target photon‑loss and rotation errors; key tools are displacement operators, modular syndrome measurements, Gaussian encoding circuits and concatenation with surface codes for thresholds; experiments often extract only the first syndrome bit yet still improve lifetime.
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