Concatenated bosonic code 

Description

A concatenated code whose inner code is a bosonic code.

Decoding

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

Parents

Child

Cousins

  • 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 Construction A.
  • Oscillator-into-oscillator GKP code — Oscillator-into-oscillator GKP 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].

References

[1]
L. Berent et al., “Analog information decoding of bosonic quantum LDPC codes”, (2023) arXiv:2311.01328
[2]
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
[3]
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
[4]
B. Royer, S. Singh, and S. M. Girvin, “Encoding Qubits in Multimode Grid States”, PRX Quantum 3, (2022) arXiv:2201.12337 DOI
[5]
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. https://errorcorrectionzoo.org/c/oscillators_concatenated
BibTeX:
@incollection{eczoo_oscillators_concatenated, title={Concatenated bosonic code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/oscillators_concatenated} }
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Cite as:

“Concatenated bosonic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/oscillators_concatenated

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/concatenated/oscillators_concatenated.yml.