Description
A concatenated \(n\)-mode code whose outer code is a quantum repetition code and whose inner code is the cat code in its cat basis.
A basis of codewords for the two-component case, \begin{align} |\overline{\pm}\rangle\propto\left(\left|\alpha\right\rangle \pm\left|-\alpha\right\rangle \right)^{\otimes n} \tag*{(1)}\end{align} for any complex \(\alpha\).
Protection
The code can detect arbitrary losses in up to \(n/2\) modes. The cat-repetition code on a 2D mode lattice is a candidate for a memory that may be self-correcting, but only in the limit of infinite energy per mode [3].
Realizations
Superconducting circuit devices: a repetition code out of two-component cat qubits has been realized for distances 3 and 5 [4].
Parent
- Concatenated cat code — The cat repetition code is a concatenation whose inner code is the cat code in its cat basis.
Child
- Cat code — The cat-repetition code for \(n=1\) reduces to the cat code.
Cousins
- Quantum repetition code — Two-component cat codes in the cat-state basis have been concatenated with quantum repetition codes [1,2,5–7].
- Self-correcting quantum code — The cat-repetition code on a 2D mode lattice is a candidate for a memory that may be self-correcting, but only in the limit of infinite energy per mode [3].
- Coherent-state 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 \(n=1\).
References
- [1]
- J. Guillaud and M. Mirrahimi, “Repetition Cat Qubits for Fault-Tolerant Quantum Computation”, Physical Review X 9, (2019) arXiv:1904.09474 DOI
- [2]
- S. Puri et al., “Bias-preserving gates with stabilized cat qubits”, Science Advances 6, (2020) arXiv:1905.00450 DOI
- [3]
- S. Lieu, Y.-J. Liu, and A. V. Gorshkov, “Candidate for a passively protected quantum memory in two dimensions”, (2023) arXiv:2205.09767
- [4]
- H. Putterman et al., “Hardware-efficient quantum error correction using concatenated bosonic qubits”, (2024) arXiv:2409.13025
- [5]
- J. Guillaud and M. Mirrahimi, “Error rates and resource overheads of repetition cat qubits”, Physical Review A 103, (2021) arXiv:2009.10756 DOI
- [6]
- C. Chamberland et al., “Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes”, PRX Quantum 3, (2022) arXiv:2012.04108 DOI
- [7]
- F.-M. L. Régent, C. Berdou, Z. Leghtas, J. Guillaud, and M. Mirrahimi, “High-performance repetition cat code using fast noisy operations”, Quantum 7, 1198 (2023) arXiv:2212.11927 DOI
Page edit log
- Victor V. Albert (2024-12-06) — most recent
Cite as:
“Cat-repetition code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cat_repetition