Description
A generalization of the 3D surface code to modular qudits. Qudits are placed on edges, \(Z\)-type stabilizer generators are placed on square plaquettes oriented in all three directions, and \(X\)-type stabilizers are placed on the six edges neighboring every vertex [1].Primary Hierarchy
Parents
A quantum triple model for the group \(G=\mathbb{Z}_q\) is a modular-qudit 3D surface code.
Generalized homological-product CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
The modular-qudit 3D surface code realizes 3D \(\mathbb{Z}_q\) gauge theory with bosonic charge and loop excitations (BcBl).
Modular-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 [3].
References
- [1]
- H. Moradi and X.-G. Wen, “Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations”, Physical Review B 91, (2015) arXiv:1404.4618 DOI
- [2]
- C. Lee, Y. Hu, G. Y. Cho, and H. Watanabe, “\(\mathbb{Z}_N\) generalizations of three-dimensional stabilizer codes”, (2025) arXiv:2504.09847
- [3]
- 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:
“Modular-qudit 3D surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_3d_surface