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

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

Five-qubit perfect code

References

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

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.