Three-rotor code[1] 

Description

\([[3,1,2]]_{\mathbb Z}\) rotor code that is an extension of the \([[3,1,2]]_3\) qutrit CSS code to the integer alphabet, i.e., the angular momentum states of a planar rotor. The code is \(U(1)\)-covariant and its ideal codewords, \begin{align} |\overline{x}\rangle = \sum_{y\in\mathbb{Z}} \left| -3y,y-x,2(y+x) \right\rangle~, \tag*{(1)}\end{align} where \(x\in\mathbb{Z}\), are not normalizable.

Protection

Normalized codewords approximately protect against erasure while maintaining covariance [2].

Parents

Cousin

References

[1]
P. Hayden et al., “Error Correction of Quantum Reference Frame Information”, PRX Quantum 2, (2021) arXiv:1709.04471 DOI
[2]
P. Faist et al., “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI
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Zoo Code ID: rotor_3_1_2

Cite as:
“Three-rotor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rotor_3_1_2
BibTeX:
@incollection{eczoo_rotor_3_1_2, title={Three-rotor code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rotor_3_1_2} }
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Permanent link:
https://errorcorrectionzoo.org/c/rotor_3_1_2

Cite as:

“Three-rotor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rotor_3_1_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/rotors/stabilizer/css/rotor_3_1_2.yml.