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Single-mode bosonic code

Description

Encodes a \(K\)-dimensional Hilbert space into a single bosonic mode. A trivial single-mode code encoding a qubit into the first two Fock states \(\{|0\rangle,|1\rangle\}\) is called the single-rail encoding [1,2].

Cousin

  • Dual-rail quantum code— Using the concatenation convention of the Zoo, concatenating the inner dual-rail code with an outer single-mode bosonic code yields several gates that are independent of the outer code [3].

Member of code lists

Primary Hierarchy

Quantum Domain
Bosonic Kingdom
Bosonic codeQECC Quantum
Qudit-into-oscillator code
Parents
Qudit-into-oscillator code
Monolithic quantum codeQECC Quantum
Single-mode bosonic code
Children
Bosonic \(q\)-ary expansion
Chebyshev code
Bosonic rotation code
Squeezed cat code
Square-lattice GKP code
Hexagonal GKP code
Squeezed Fock-state code

References

[1]
H.-W. Lee and J. Kim, “Quantum teleportation and Bell’s inequality using single-particle entanglement”, Physical Review A 63, (2000) arXiv:quant-ph/0007106 DOI
[2]
A. P. Lund and T. C. Ralph, “Nondeterministic gates for photonic single-rail quantum logic”, Physical Review A 66, (2002) arXiv:quant-ph/0205044 DOI
[3]
H.-K. Lau and M. B. Plenio, “Universal Quantum Computing with Arbitrary Continuous-Variable Encoding”, Physical Review Letters 117, (2016) arXiv:1605.09278 DOI
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Zoo Code ID: single-mode

Cite as:
“Single-mode bosonic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/single-mode, arXiv:2606.11484
BibTeX:
@incollection{eczoo_single-mode,
title={Single-mode bosonic code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/single-mode}
}
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Permanent link:
https://errorcorrectionzoo.org/c/single-mode

Cite as:

“Single-mode bosonic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/single-mode, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/single-mode.yml.