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.
Parents
Children
- Quantum rainbow code — Quantum pin codes are defined for simplicial complexes that admit certain colorings [1].
- Dinur-Hsieh-Lin-Vidick (DHLV) code
- Fiber-bundle code
- Lossless expander balanced-product code
- Bicycle code
- Bivariate bicycle (BB) code
- Quantum check-product code
- Dinur-Lin-Vidick (DLV) code
- Generalized quantum Tanner code
- Lift-connected surface (LCS) code
- Tensor-product HDX code — Tensor-product HDX codes result from a iterated tensor products of Ramanujan complexes.
- Homological code — 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.
Cousins
- Cyclic linear binary code — Iterative tensor-product codes can be constructed out of CSS codes that in turn stem from cyclic codes [2].
- Quantum Reed-Muller code — Iterative tensor-product codes can be constructed out of quantum Reed-Muller codes [2].
- Quantum pin code — One can construct quantum pin codes from any chain complex [3; 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 \(n\) [2].
References
- [1]
- T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes”, (2024) arXiv:2408.13130
- [2]
- B. Audoux and A. Couvreur, “On tensor products of CSS Codes”, (2018) arXiv:1512.07081
- [3]
- 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