Description
A concatenated \(n\)-mode code (for odd \(n\)) whose outer code is a quantum repetition code and whose inner code is the two-component cat code in its coherent-state basis.
A basis of codewords is \begin{align} |\overline{\pm}\rangle\propto\left|\pm\alpha\right\rangle ^{\otimes n} \tag*{(1)}\end{align} for any complex \(\alpha\).
Protection
The code cannot protect against losses and has a minimum Euclidean distance \(d_Z = 4n\) [3].
Parents
- Concatenated cat code — The coherent-state repetition code is a concatenation whose inner code is the cat code in its coherent-state basis.
- Tiger code — The coherent-state repetition code is a tiger code whose matrix \(G\) is a generator matrix of the repetition code (over the integers), and whose matrix \(H\) is zero [3].
Child
- Two-component cat code — The coherent-state repetition code for \(n=1\) reduces to the two-component cat code.
Cousins
- Cat-repetition code — The cat (coherent-state) repetition code is a concatenation whose inner code is the (two-component) cat code in its cat (coherent-state) basis. For the two-component case, both reduce to the two-component cat code at \(n=1\).
- Quantum repetition code — Two-component cat codes in the coherent-state basis have been concatenated with quantum repetition codes [1,2].
References
- [1]
- H. Jeong and M. S. Kim, “Efficient quantum computation using coherent states”, Physical Review A 65, (2002) arXiv:quant-ph/0109077 DOI
- [2]
- T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states”, Physical Review A 68, (2003) arXiv:quant-ph/0306004 DOI
- [3]
- Y. Xu, Y. Wang, C. Vuillot, and V. V. Albert, “Letting the tiger out of its cage: bosonic coding without concatenation”, (2024) arXiv:2411.09668
Page edit log
- Victor V. Albert (2024-12-06) — most recent
Cite as:
“Coherent-state repetition code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/coherent_state_repetition