Description
CSS code constructed from a tensor code. In some cases, only one of the classical codes forming the tensor code needs to be self-orthogonal.Protection
If one of the classical codes forming the tensor code protects against burst errors, the resulting quantum code does also [2].Cousins
- Tensor-product code— Quantum tensor-product codes are quantum analogues of tensor-product codes.
- Reversible code— Reversible cyclic codes can be used to construct quantum tensor-product codes [2].
- Cyclic linear \(q\)-ary code— Reversible cyclic codes can be used to construct quantum tensor-product codes [2].
- Maximum distance separable (MDS) code— MDS codes can be used to construct quantum tensor-product codes [2].
- Galois-qudit RS code— Product codes constructed from a self-orthogonal and an arbitrary RS code yield an RS code [1].
- Quantum check-product code— Quantum check-product codes extend the concept of a check product, which yields the dual of a tensor code, to a product between a classical and a quantum code.
- Quantum Reed-Muller (RM) code— EA versions of quantum RM codes and their quantum tensor-product variants can be constructed [3].
Member of code lists
Primary Hierarchy
References
- [1]
- M. Grassl and M. Rotteler, “Quantum block and convolutional codes from self-orthogonal product codes”, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. 1018 (2005) arXiv:quant-ph/0703181 DOI
- [2]
- J. Fan, Y. Li, M.-H. Hsieh, and H. Chen, “On Quantum Tensor Product Codes”, (2017) arXiv:1605.09598
- [3]
- P. J. Nadkarni, P. Jayakumar, A. Behera, and S. S. Garani, “Entanglement-assisted Quantum Reed-Muller Tensor Product Codes”, Quantum 8, 1329 (2024) arXiv:2303.08294 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-07-18)
Cite as:
“Quantum tensor-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_tensor_product, arXiv:2606.11484