Concatenated bosonic code 

Description

A concatenated code whose outer code is a bosonic code. In other words, a bosonic code that can be thought of as a concatenation of a possibly non-bosonic inner code and another bosonic outer code.

Decoding

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

Parents

  • Bosonic code
  • Concatenated quantum code — A concatenated bosonic code is a bosonic code that can be thought of as a concatenation of a possibly non-bosonic outer code and another bosonic inner code.

Children

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].
  • Dual-rail quantum code — The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code [4]. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code [5] that protects against \(d-1\) AD errors [6]. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code [7].
  • Two-mode binomial code — Two-mode binomial codes can be concatenated with repetition codes to yield bosonic analogues of QPCs [8].
  • Hybrid cat code — Hybrid cat codes can be concatenated with RBH codes [9].

References

[1]
L. Berent, T. Hillmann, J. Eisert, R. Wille, and J. Roffe, “Analog Information Decoding of Bosonic Quantum Low-Density Parity-Check Codes”, PRX Quantum 5, (2024) arXiv:2311.01328 DOI
[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) 2499 (2016) DOI
[4]
E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics”, Nature 409, 46 (2001) DOI
[5]
Y. Ouyang, “Avoiding coherent errors with rotated concatenated stabilizer codes”, npj Quantum Information 7, (2021) arXiv:2010.00538 DOI
[6]
R. Duan, M. Grassl, Z. Ji, and B. Zeng, “Multi-error-correcting amplitude damping codes”, 2010 IEEE International Symposium on Information Theory (2010) arXiv:1001.2356 DOI
[7]
H.-K. Lau and M. B. Plenio, “Universal Quantum Computing with Arbitrary Continuous-Variable Encoding”, Physical Review Letters 117, (2016) arXiv:1605.09278 DOI
[8]
M. Bergmann and P. van Loock, “Quantum error correction against photon loss using NOON states”, Physical Review A 94, (2016) arXiv:1512.07605 DOI
[9]
J. Lee, N. Kang, S.-H. Lee, H. Jeong, L. Jiang, and S.-W. Lee, “Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons”, (2023) arXiv:2401.00450
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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/oscillators_concatenated.yml.