\([[3,1,2]]_{\mathbb Z}\) rotor code

\([[3,1,2]]_{\mathbb Z}\) rotor code[1]

Description

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 ideal codewords are not normalizable.

Protection

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

Parents

Rotor code
Covariant code — The \([[3,1,2]]_{\mathbb Z}\) code is \(U(1)\)-covariant.

Cousin

Three qutrit code

References

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

Cite as:

“\([[3,1,2]]_{\mathbb Z}\) 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/tree/main/codes/quantum/groups/rotor_3_1_2.yml.