\((1,3)\) 4D toric code[1]
Description
A generalization of the Kitaev surface code defined on a 4D lattice. The code is called a \((1,3)\) toric code because it admits 1D \(Z\)-type and 3D \(X\)-type logical operators.
Transversal Gates
Logical \(CCCZ\) gate on a hyper-diamond lattice [1].
Parents
- Homological code — The \((1,3)\) 4D toric code realizes 4D \(\mathbb{Z}_2\) gauge theory with 1D \(Z\)-type and 3D \(X\)-type logical operators.
- Lattice stabilizer code
- Abelian topological code — The \((1,3)\) 4D toric code realizes 4D \(\mathbb{Z}_2\) gauge theory with 1D \(Z\)-type and 3D \(X\)-type logical operators.
Cousin
- \(D_4\) hyper-diamond lattice code — The \((1,3)\) 4D toric code on a hyper-diamond lattice admits a transversal logical \(CCCZ\) gate [1].
References
- [1]
- T. Jochym-O’Connor and T. J. Yoder, “Four-dimensional toric code with non-Clifford transversal gates”, Physical Review Research 3, (2021) arXiv:2010.02238 DOI
Page edit log
- Victor V. Albert (2024-07-10) — most recent
- Nathanan Tantivasadakarn (2024-07-10)
Cite as:
“\((1,3)\) 4D toric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/4d_13_surface