XYZ product code[1]

Description

A non-CSS QLDPC code constructed from three classical codes. The construction of an XYZ product code is similar to that of a hypergraph product code and related codes. The idea is that rather than taking a product of only two classical codes to produce a CSS code, a third classical code is considered, acting with Pauli-\(Y\) operators.

Rate

Not much has been proven about the relationship between XYZ-product codes and other codes. The logical dimension depends on properties of the input classical codes, specifically similarity invariants from abstract algebra. It is conjectured that specific instances of XYZ-product codes have a constant encoding rate and a minimum distance of \(d \in \Theta(n^{2/3})\) [1].

Parents

Cousin

Zoo code information

Internal code ID: xyz_product

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: xyz_product

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

References

[1]
Anthony Leverrier, Simon Apers, and Christophe Vuillot, “Quantum XYZ Product Codes”. 2011.09746

Cite as:

“XYZ product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/xyz_product

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