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].
Parent
- Generalized homological product code — XYZ product codes result from a tensor product of three classical-code chain complexes.
Cousin
- Hypergraph product code — The XYZ product code is based on a hypergraph product of three classical codes.
References
- [1]
- A. Leverrier, S. Apers, and C. Vuillot, “Quantum XYZ Product Codes”, Quantum 6, 766 (2022) arXiv:2011.09746 DOI
Page edit log
- Finnegan Voichick (2021-12-01) — most recent
Cite as:
“XYZ product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/xyz_product