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.

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 [25]) can be highly biased toward one type of noise while still ensuring good performance.

A concatenation of the repetition code with the two-component cat code is a candidate for a memory that may be self-correcting, but only in the limit of infinite energy per mode [6].

Realizations

Superconducting circuit devices: a repetition code out of two-component cat qubits has been realized for distances 3 and 5 [7].

Parent

Cousins

  • Quantum repetition code — Two-component cat codes have been concatenated with quantum repetition codes [25,8].
  • Rotated surface code — Cat codes have been concatenated with rotated surface codes [8].
  • Low-density parity-check (LDPC) code — Cat codes have been concatenated with LDPC codes (treated as qubit stabilizer codes) [9].
  • Lechner-Hauke-Zoller (LHZ) code — LHZ parity-codes have been concatenated with cat codes [10].
  • \([[7,1,3]]\) 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 \(\alpha > 1.2\) [11].
  • 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 \(\alpha > 1.2\) [11].
  • Self-correcting quantum code — A concatenation of the repetition code with the two-component cat code is a candidate for a memory that may be self-correcting, but only in the limit of infinite energy per mode [6].
  • 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 et al., “High-performance repetition cat code using fast noisy operations”, Quantum 7, 1198 (2023) arXiv:2212.11927 DOI
[6]
S. Lieu, Y.-J. Liu, and A. V. Gorshkov, “Candidate for a passively protected quantum memory in two dimensions”, (2023) arXiv:2205.09767
[7]
H. Putterman et al., “Hardware-efficient quantum error correction using concatenated bosonic qubits”, (2024) arXiv:2409.13025
[8]
C. Chamberland et al., “Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes”, PRX Quantum 3, (2022) arXiv:2012.04108 DOI
[9]
D. Ruiz et al., “LDPC-cat codes for low-overhead quantum computing in 2D”, (2024) arXiv:2401.09541
[10]
A. Messinger et al., “Fault-tolerant quantum computing with the parity code and noise-biased qubits”, (2024) arXiv:2404.11332
[11]
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

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: cat_concatenated

Cite as:
“Concatenated cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cat_concatenated
BibTeX:
@incollection{eczoo_cat_concatenated, title={Concatenated cat code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/cat_concatenated} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/cat_concatenated

Cite as:

“Concatenated cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/cat_concatenated

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/coherent_state/cat/cat_concatenated.yml.