Concatenated cat code[1]
Description
A concatenated code whose outer code is a cat code. In other words, a qubit code that can be thought of as a concatenation of an arbitrary inner code and another cat outer code. Most examples encode physical qubits of an inner stabilizer code into the two-component cat code in its cat-state basis.
Protection
The cat code suppresses dephasing errors exponentially with the size of its coherent states, so the inner code (e.g., a quantum repetition code [2–5]) can be highly biased toward one type of noise while still ensuring good performance.
Parents
Children
- Cat-repetition code — The cat repetition code is a concatenation whose inner code is the cat code in its cat basis.
- Coherent-state repetition code — The coherent-state repetition code is a concatenation whose inner code is the cat code in its coherent-state basis.
Cousins
- Rotated surface code — Cat codes have been concatenated with rotated surface codes [6].
- Low-density parity-check (LDPC) code — Cat codes have been concatenated with LDPC codes (treated as qubit stabilizer codes) [7].
- Lechner-Hauke-Zoller (LHZ) code — LHZ parity-codes have been concatenated with cat codes [8].
- \([[7,1,3]]\) Steane code — Two-component cat codes concatenated with Steane and Golay codes are estimated to be fault tolerant against photon loss noise with rate \(\eta < 5\times 10^{-4}\) provided that \(\alpha > 1.2\) [9].
- \([[23, 1, 7]]\) Quantum Golay code — Two-component cat codes concatenated with Steane and Golay codes are estimated to be fault tolerant against photon loss noise with rate \(\eta < 5\times 10^{-4}\) provided that \(\alpha > 1.2\) [9].
- Quantum spherical code (QSC) — CSS codes concatenated with two-component cat codes form QSCs which have a weight-based notion of distance.
References
- [1]
- J. Cohen and M. Mirrahimi, “Dissipation-induced continuous quantum error correction for superconducting circuits”, Physical Review A 90, (2014) arXiv:1409.6759 DOI
- [2]
- J. Guillaud and M. Mirrahimi, “Repetition Cat Qubits for Fault-Tolerant Quantum Computation”, Physical Review X 9, (2019) arXiv:1904.09474 DOI
- [3]
- S. Puri et al., “Bias-preserving gates with stabilized cat qubits”, Science Advances 6, (2020) arXiv:1905.00450 DOI
- [4]
- J. Guillaud and M. Mirrahimi, “Error rates and resource overheads of repetition cat qubits”, Physical Review A 103, (2021) arXiv:2009.10756 DOI
- [5]
- 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
- [6]
- C. Chamberland et al., “Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes”, PRX Quantum 3, (2022) arXiv:2012.04108 DOI
- [7]
- D. Ruiz, J. Guillaud, A. Leverrier, M. Mirrahimi, and C. Vuillot, “LDPC-cat codes for low-overhead quantum computing in 2D”, (2024) arXiv:2401.09541
- [8]
- A. Messinger, V. Torggler, B. Klaver, M. Fellner, and W. Lechner, “Fault-tolerant quantum computing with the parity code and noise-biased qubits”, (2024) arXiv:2404.11332
- [9]
- A. P. Lund, T. C. Ralph, and H. L. Haselgrove, “Fault-Tolerant Linear Optical Quantum Computing with Small-Amplitude Coherent States”, Physical Review Letters 100, (2008) arXiv:0707.0327 DOI
Page edit log
- Victor V. Albert (2024-07-17) — most recent
Cite as:
“Concatenated cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cat_concatenated