Qudit 3D surface code[1]
Description
A generalization of the 3D surface code to modular qudits.Primary Hierarchy
Parents
Generalized homological-product CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
The qudit 3D surface code realizes 3D \(\mathbb{Z}_q\) gauge theory with bosonic charge and loop excitations (BcBl).
Qudit 3D surface code
Children
The qudit 3D surface code reduces to the 3D surface code for \(q=2\). The 3D surface code realizes 3D \(\mathbb{Z}_2\) gauge theory with bosonic charge and loop excitations (BcBl). The welded surface code does not satisfy homogeneous topological order [2].
References
- [1]
- C. Lee, Y. Hu, G. Y. Cho, and H. Watanabe, “\(\mathbb{Z}_N\) generalizations of three-dimensional stabilizer codes”, (2025) arXiv:2504.09847
- [2]
- J. Haah, “A degeneracy bound for homogeneous topological order”, SciPost Physics 10, (2021) arXiv:2009.13551 DOI
Page edit log
- Victor V. Albert (2024-04-20) — most recent
Cite as:
“Qudit 3D surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_3d_surface