Description
A qubit CSS code whose properties are determined from an underlying chain complex via the qubit CSS-to-homology correspondence. This complex often consists of some type of product of other chain complexes.Cousin
- Quantum pin code— One can construct quantum pin codes from any chain complex [1; Sec. II.F].
Primary Hierarchy
Parents
Homological products are a primary tool for generating qubit QLDPC codes with favorable parameters. Typically, whenever the input codes are binary LDPC or qubit QLDPC, the resulting code will be qubit QLDPC with non geometrically local stabilizer generators.
Generalized homological-product CSS codeGeneralized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS code
Children
DLV codes are codes constructed using a cubical chain complex, which is a \(t\)-order extension of the chain complexes underlying quantum generalized homological product CSS codes.
The generalized surface code is constructed from chain complexes arising from cell complexes of the underlying manifold. Such complexes are not necessarily products of two non-trivial complexes, but the manifolds are picked so that their homology ensures favorable code properties.
References
- [1]
- C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
Page edit log
- Victor V. Albert (2023-11-13) — most recent
Cite as:
“Generalized homological-product qubit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_generalized_homological_product_css