Fiber-bundle code[1]

Description

CSS code constructed by combining a random LDPC code as the base and a cyclic repetition code as the fiber of a fiber bundle. After applying distance balancing, a QLDPC code with distance \(\Omega(n^{3/5}\text{polylog}(n))\) and rate \(\Omega(n^{-2/5}\text{polylog}(n))\) is obtained.

Rate

Rate \(k/n = \Omega(n^{-2/5}/\text{polylog}(n))\), distance \(d=\Omega(n^{3/5}/\text{polylog}(n))\). This is the first QLDPC code to achieve a distance scaling better than \(\sqrt{n}~\text{polylog}(n)\).

Decoding

Greedy algorithm can be used to efficiently decode \(X\) errors, but no known efficient decoding of \(Z\) errors yet [1].

Parent

Child

Cousins

Zoo code information

Internal code ID: fiber_bundle

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: fiber_bundle

Cite as:
“Fiber-bundle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fiber_bundle
BibTeX:
@incollection{eczoo_fiber_bundle, title={Fiber-bundle code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/fiber_bundle} }
Permanent link:
https://errorcorrectionzoo.org/c/fiber_bundle

References

[1]
Matthew B. Hastings, Jeongwan Haah, and Ryan O'Donnell, “Fiber Bundle Codes: Breaking the $N^{1/2} \operatorname{polylog}(N)$ Barrier for Quantum LDPC Codes”. 2009.03921
[2]
N. P. Breuckmann and J. N. Eberhardt, “Balanced Product Quantum Codes”, IEEE Transactions on Information Theory 67, 6653 (2021). DOI; 2012.09271

Cite as:

“Fiber-bundle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/fiber_bundle

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/qldpc/fiber_bundle.yml.