\([[5,1,3]]_{\mathbb Z}\) 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
- Rotor code
- Covariant code — The \([[5,1,3]]_{\mathbb Z}\) code is \(U(1)\)-covariant.
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
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.