Four-rotor code[1; Sec. VIII]
Description
\([[4,2,2]]_{\mathbb Z}\) CSS rotor code that is an extension of the four-qubit code to the integer alphabet, i.e., the angular momentum states of a planar rotor.
The code is \(U(1)\)-covariant and its ideal logical-rotor codewords, \begin{align} |\overline{x,y}\rangle = \sum_{j,k,l\in\mathbb{Z}} \delta_{a,j+k}\delta_{b,l} \left| j,k,j+l,k+l \right\rangle~, \tag*{(1)}\end{align} where \(a,b\in\mathbb{Z}\), are not normalizable.
Parents
- Homological rotor code
- \([[4,2,2]]_{G}\) four group-qudit code — The four group-qudit code reduces to the four-rotor code for \(G= \mathbb{Z}\).
References
- [1]
- P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, “Continuous Symmetries and Approximate Quantum Error Correction”, Physical Review X 10, (2020) arXiv:1902.07714 DOI
Page edit log
- Victor V. Albert (2023-11-05) — most recent
Cite as:
“Four-rotor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/rotor_4_2_2