Concatenated bosonic code 


A concatenated code whose inner code is a bosonic code.


Decoder exploiting analog information from the inner code for bosonic codes concatenated with qubit QLDPC codes [1].




  • Coherent-state constellation code — Coherent-state constellation codes consisting of points from a Gaussian quadrature rule can be concatenated with quantum polar codes to achieve the Gaussian coherent information of the thermal noise channel [2,3].
  • Quantum spherical code (QSC) — CSS codes concatenated with two-component cat codes form QSCs which have a weight-based notion of distance.
  • \(D_4\) hyper-diamond GKP code — The \(D_4\) hyper-diamond GKP code can be seen as a concatenation of a rotated square-lattice GKP code with a repetition code [4]. This is related to the fact that the four-bit repetition code yields the \(D_4\) hyper-diamond lattice code via the mod-two lattice construction.
  • GKP-stabilizer code — GKP-stabilizer oscillator-into-oscillator codes concantenated with GKP qubit-into-mode codes can outperform the more conventional concatenations of GKP codes with qubit stabilizer codes [5].


L. Berent et al., “Analog information decoding of bosonic quantum LDPC codes”, (2023) arXiv:2311.01328
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent-state constellations and polar codes for thermal Gaussian channels”, Physical Review A 95, (2017) arXiv:1603.05970 DOI
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent state constellations for Bosonic Gaussian channels”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) DOI
B. Royer, S. Singh, and S. M. Girvin, “Encoding Qubits in Multimode Grid States”, PRX Quantum 3, (2022) arXiv:2201.12337 DOI
Y. Xu et al., “Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison”, PRX Quantum 4, (2023) arXiv:2209.04573 DOI
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Zoo Code ID: oscillators_concatenated

Cite as:
“Concatenated bosonic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_oscillators_concatenated, title={Concatenated bosonic code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Cite as:

“Concatenated bosonic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.