Description
Qubit CSS code whose properties are determined from an underlying chain complex, which often consists of some type of product of other chain complexes.Cousins
- Cyclic linear binary code— Iterative tensor-product codes can be constructed out of CSS codes that in turn stem from cyclic codes [1].
- Quantum Reed-Muller code— Iterative tensor-product codes can be constructed out of quantum Reed-Muller codes [1].
- Quantum pin code— One can construct quantum pin codes from any chain complex [2; Sec. II.F].
- Finite-geometry (FG) QLDPC code— Iterative tensor products of PG-QLDPC codes yield codes whose stabilizer-generator weights scale almost logarithmically with \(n\) [1].
Primary Hierarchy
Parents
Generalized homological-product CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS code
Children
Quantum pin codes are defined for simplicial complexes that admit certain colorings [3].
Tensor-product HDX codes result from a iterated tensor products of Ramanujan complexes.
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]
- B. Audoux and A. Couvreur, “On tensor products of CSS Codes”, (2018) arXiv:1512.07081
- [2]
- C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
- [3]
- T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes”, (2024) arXiv:2408.13130
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