Qudit cubic code[13] 

Description

Generalization of the Haah cubic code to modular qudits.

Protection

Performance over the erasure and depolarizing channels was studied in Ref. [4].

Parents

  • Modular-qudit stabilizer code
  • Fracton stabilizer code — Haah cubic [5] codes 1-4, 7, 8, and 10 do not have string logical operators and are the first examples of Type-II fracton phases. The remaining cubic codes are fractal Type-I fracton codes [6,7]. There is evidence that a qutrit and a \(q=5\) qudit cubic code from Ref. [1] have no string operators and are thus Type-II fracton codes (see [6; Eqs. (D11-D13)]).

Child

Cousins

References

[1]
I. H. Kim, “3D local qupit quantum code without string logical operator”, (2012) arXiv:1202.0052
[2]
J. Haah, Two generalizations of the cubic code model, KITP Conference: Frontiers of Quantum Information Physics, UCSB, Santa Barbara, CA.
[3]
V. V. Albert, S. Pascazio, and M. H. Devoret, “General phase spaces: from discrete variables to rotor and continuum limits”, Journal of Physics A: Mathematical and Theoretical 50, 504002 (2017) arXiv:1709.04460 DOI
[4]
A. J. Moncy and P. Kiran Sarvepalli, “Performance of Nonbinary Cubic Codes”, 2018 International Symposium on Information Theory and Its Applications (ISITA) (2018) DOI
[5]
J. Haah, “Local stabilizer codes in three dimensions without string logical operators”, Physical Review A 83, (2011) arXiv:1101.1962 DOI
[6]
A. Dua et al., “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
[7]
M. Pretko, X. Chen, and Y. You, “Fracton phases of matter”, International Journal of Modern Physics A 35, 2030003 (2020) arXiv:2001.01722 DOI
Page edit log

Your contribution is welcome!

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

edit on this site

Zoo Code ID: qudit_cubic

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits/topological/fracton/qudit_cubic.yml.