\([[5,1,3]]_{\mathbb Z}\) 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].

Parents

Cousin

References

[1]
P. Faist et al., “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020). DOI; 1902.07714

Zoo code information

Internal code ID: rotor_5_1_3

Your contribution is welcome!

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Zoo Code ID: rotor_5_1_3

Cite as:
“\([[5,1,3]]_{\mathbb Z}\) 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={\([[5,1,3]]_{\mathbb Z}\) 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:

“\([[5,1,3]]_{\mathbb Z}\) 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/tree/main/codes/quantum/groups/rotor_5_1_3.yml.