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Five-rotor code[1]

Description

Extension of the five-qubit stabilizer code to the integer alphabet, i.e., the angular momentum states of a planar rotor. The code is \(U(1)\)-covariant and ideal codewords are not normalizable.

Protection

Normalized codewords approximately protect against erasure while maintaining covariance [1].

Cousin

Member of code lists

Primary Hierarchy

Quantum Domain
Group Kingdom
Group-based quantum codeQECC Quantum
Rotor code
Rotor stabilizer codeStabilizer Hamiltonian-based QECC Quantum
Parents
Rotor stabilizer code
Covariant block quantum codeQECC Quantum
The five-rotor code is \(U(1)\)-covariant.
Perfect-tensor codeQECC Quantum
Five-rotor codewords are CV AME [2].
Cyclic quantum codeQECC Quantum
Small-distance block quantum codeQECC Quantum
Five-rotor code

References

[1]
P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI
[2]
J. I. Kwon, A. J. Brady, and V. V. Albert, “Most continuous-variable cluster states are too entangled to be useless”, (2025) arXiv:2503.15698
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Zoo Code ID: rotor_5_1_3

Cite as:
“Five-rotor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rotor_5_1_3
BibTeX:
@incollection{eczoo_rotor_5_1_3, title={Five-rotor code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rotor_5_1_3} }
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Permanent link:
https://errorcorrectionzoo.org/c/rotor_5_1_3

Cite as:

“Five-rotor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rotor_5_1_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/rotors/stabilizer/rotor_5_1_3.yml.