[Jump to code hierarchy]

4D lattice stabilizer code

Description

Lattice stabilizer code in four Euclidean dimensions, using either the ordinary block notion of locality or the fermionic/Majorana notion of locality.

Cousin

Member of code lists

Primary Hierarchy

Quantum Domain
Group quantum Kingdom
Group-based quantum codeQECC Quantum
Stabilizer codeHamiltonian-based QECC Quantum
Quantum low-weight check (QLWC) codeQECC Quantum
QLDPC code
Lattice stabilizer code
Parents
Lattice stabilizer code
4D lattice stabilizer code
Children
\(D_4\) hyper-diamond GKP code
\([[16,6,4]]\) Tesseract color code
The tesseract color code is a 4D color code defined on a tesseract [2–5].
\((1,3)\) 4D toric code
\((2,2)\) Loop toric code

References

[1]
B. Royer, S. Singh, and S. M. Girvin, “Encoding Qubits in Multimode Grid States”, PRX Quantum 3, (2022) arXiv:2201.12337 DOI
[2]
M. B. Hastings, “Small Majorana Fermion Codes”, (2017) arXiv:1703.00612
[3]
J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, “Magic state distillation with low space overhead and optimal asymptotic input count”, Quantum 1, 31 (2017) arXiv:1703.07847 DOI
[4]
N. Delfosse and B. W. Reichardt, “Short Shor-style syndrome sequences”, (2020) arXiv:2008.05051
[5]
P. Prabhu and B. W. Reichardt, “Distance-four quantum codes with combined postselection and error correction”, Physical Review A 110, (2024) arXiv:2112.03785 DOI
Page edit log

Your contribution is welcome!

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

edit on this site

Zoo Code ID: 4d_stabilizer

Cite as:
“4D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/4d_stabilizer
BibTeX:
@incollection{eczoo_4d_stabilizer, title={4D lattice stabilizer code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/4d_stabilizer} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/4d_stabilizer

Cite as:

“4D lattice stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/4d_stabilizer

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/stabilizer/lattice/4d_stabilizer.yml.